Why did the United States, after two and one half years of neutrality, entered the stalemated, horrifically costly, World War I?

I was responding to a comment in here when it was deleted. I'll just keep my formatting since it was how I intended to go over it anyways.

One of the largest reasons was that the United States made a much larger investment in the Allied side than with the Central Powers. Between loans, the selling of arms, and previous interactions with Britain and France, they had invested a lot of time and money into the Allied side. The money was used for weapons production, technological innovations, and general upkeep of their countries. Part of the reason they entered the war was to make sure their investment succeeded, and that they would be paid back by the Allied Countries.

This was previously included in an answer, and I can agree with it.

However, some other major factors forced the United States to take the Allied side was the due in large part to the actions of the Germans. They made American neutrality essentially impossible.

Alright, still good.

Germany talked a lot of smack against America, stating that they were not a major power and things of that nature.

I mean, not a big deal to the US, but sure. I wouldn't count this as a main reason, or even a big one at all.

The Germans also declared unrestricted submarine warfare, which would sink any enemy ship no matter if it was for war or not.

Almost undoubtedly the biggest factor, I'd say. I'll get to that in more detail later.

Due to these actions, Germany tried (at least, allegedly) to persuade Mexico to occupy the United States with war so that they could not join the Allies in the fight against the Central Powers.

It's not alleged. Zimmerman went on to give a speech explaining his side of the story, and admitting that he did send the telegram. He said:

It is being investigated how these instructions fell into the hands of the American authorities. I instructed the Minister to Mexico, in the event of war with the United States, to propose a German alliance to Mexico, and simultaneously to suggest that Japan join the alliance.

I think that's very clear insofar as the proposed alliance, and the legitimacy of the telegraph. To suggest it's not real, and that it's only "alleged" does a great disservice to the amount of information on the subject.

Germany offers Mexico a deal of financing the war and rebuilding their nation by taking back the Southern United States that they lost in the Mexican-American War.

Alright, back on track.

The telegram, known as the Zimmerman Telegram, was conveniently intercepted by the British and given to the United States at the most ideal time to try and convince the United States to come to war. It is estimated that this telegram was given to the United States by Britain and month after it was actually intercepted.

A month and a week, yes. It was sent on January 16, 1917, and sent to the US on February 23, 1917. First of all, let's understand why Germany was sending the telegram in the first place. Germany knew that they needed to resume unrestricted submarine warfare to stand a chance in the war, but also knew that doing so would lead to US involvement. They hoped to keep the US out of the war by distracting them with Mexico. That's a pretty well-known fact. As put by Doerries:

The German ambassador made it absolutely clear to the Wilhelm- strasse that the submarine order was tantamount to a declaration of war against the United States, but the Foreign Office had already written off any reconciliation with Washington and offered an alliance against America to Mexico's President Carranza.

So, knowing this, the Germans figured the American entry into the war was inevitable because of the submarine warfare being resumed. So it didn't matter if the telegram was released at a certain time, according to the Germans, because they figured war would come anyways. On March 18th, Austria (even post-Zimmerman telegram) hoped to get the US involved as a mediator. Again Doerries:

When the Austrians persisted in keeping open the channels of communication with Washington and approached Berlin concerning a possibility of excluding certain United States ships from submarine attacks, William II personally decreed: "Negotiations with America are now finished once and for all! If Wilson wants war, he can make it and then have it!"

The real kicker was the fact that neither side was in a position to budge. Germany couldn't exclude American ships from their policy, tensions were high, and the Zimmerman Telegram contributed. It certainly wasn't fabricated though. But why was it withheld for a month and a week, again?

First, let's look at how it was intercepted. It was sent in code, through both an American cable and a Swedish one (which would then take British lines to South America), as well as by German radio. The Germans had used American lines to send telegrams to the Western hemisphere, since the British cut their lines earlier in the war. One dissertation I've read says that the British were monitoring these lines, another that Western Union was pressured to give up the telegram to the Secretary of State (Robert Lansing) who passed it to the British. However it was taken to the British is of little consequence, however, because of what it said.

Now, keep in mind that the British didn't wait until unrestricted submarine warfare had just resumed to release it. They'd reportedly had it decrypted pretty fast. The real concern was that if they revealed the text, the Germans might realize that the British had broken their codes long ago. So they had to wait an appropriate amount of time, and come up with a cover story, that explained that they "intercepted it from a spy in Mexico", so it was undecoded when they got it. In fact, they did get a version of it in Mexico City on February 19th; 4 days before they handed it off to the United States.

As Winkler puts it:

The discovery of the message had put Admiral "Blinker" Hall, the head of Room 40, in a quandary. Though America's distress would serve Britain's interests, the release of the message might reveal that Britain could read Germany's codes and was monitoring neutral diplomatic traffic -- even that of the United States.

Now, if you couple the eventual release of this telegram to the US (on February 23rd), and the resumption of unrestricted submarine warfare (on January 31st), you have a toxic mix hat led the United States to feel compelled to join. After the sinking of the Lusitania in 1915, where around 130 American citizens were killed (and where tensions ran high enough that war was almost declared then), Germany attempted to claim that the ship was a warship and therefore prone to be sunk according to the laws of war at any time. However, this was not acceptable to the Americans since it was not armed and had no offensive weapons ready, meaning it was not a warship by most accounts. The Germans also took the line that they were destroying ammunition that was bound for enemies who would use it to kill their solders. Once again, the Americans didn't really care; indignation was high, no matter what international law said was allowed. The German government agreed to restrict submarine warfare grudgingly to warships and only warships, not ships that might be merchant ships carrying ammunition or the like. However, in 1916, they sank a British ship, the Sussex thinking it was laying mines. Another 50 Americans died, and the Germans agreed to make the "Sussex Pledge", which can be found here. Notes:

As the German Government repeatedly declared, it cannot dispense with the use of the submarine weapon in the conduct of warfare against enemy trade. The German Government, however, has now decided to make a further concession, adapting methods of submarine war to the interests of neutrals. In reaching its decision the German Government is actuated by considerations which are above the level of the disputed question.

Also, this order was sent out:

In accordance with the general principles of visit and search and the destruction of merchant vessels, recognized by international law, such vessels, both within and without the area declared a naval war zone, shall not be sunk without warning and without saving human lives unless the ship attempts to escape or offer resistance.

When these were effectively rescinded with the announcement of resuming submarine warfare on January 31st, it was already pretty bad. But when on February 23rd, the British finally had a way to hand over the Zimmermann Telegram without incriminating themselves and losing their code-breaking advantage, it was effectively all over. The US lost all faith in Germany letting it stay out of the war, and viewed it as a threat to US interests and citizens. In my opinion, that was without a doubt the most important coupling of events, and was the main reason for the declaration of war that followed in April (after ships were sunk, and the American public got riled up by the public release of the telegram in early March).

Sources:

The United States and Carranza, 1917: The Question of De Jure Recognition Mark T. Gilderhus The Americas, Vol. 29, No. 2 (Oct., 1972), pp. 214-231

Imperial Berlin and Washington: New Light on Germany's Foreign Policy and America's Entry into World War I Reinhard R. Doerries Central European History, Vol. 11, No. 1 (Mar., 1978), pp. 23-49

By SAMUEL, F. B. (1958, Oct 19). A wire that went awry. New York Times (1923-Current File)

Winkler, J. R. (2004). Wiring the world: United states foreign policy and global strategic communications, 1914--1921. (Order No. 3125329, Yale University). ProQuest Dissertations and Theses

The Sinking of the Lusitania Thomas A. Bailey The American Historical Review, Vol. 41, No. 1 (Oct., 1935), pp. 54-73