was it a stalemate through out until the tanks rolled in?

It ceased to really be a stalemate when the Tanks first arrived, but this was entirely coincidental. They proved a useful accessory to the infantry, but attacks could and did succeed without them.

Is there any in particular at any time that could have decided the war ... Was there any point where Germany was on the brink of victory?

There was vary much a chance for the Germans to attain a significant victory in August-September 1914, when they invaded France and Belgium. The Belgian Army was forced to retreat to Antwerp, and only escaped to the Yser River after the Marne. Likewise, the French 5th Army was occupying a salient around Namur that might have become a pocket, had the Germans been aware of the situation before Lanrezac ordered a withdrawal. The BEF suffered greatly at Mons, and was forced to stand and fight at Le Cateau against superior numbers. Had the Germans had the cavalry to envelope them, and moreover to identify openings on the flanks, they could have destroyed the BEF. With these forces indisposed, the Allied northern flank would be open for outflanking, with exception of the 9th French Army and the forces gathered around Paris. Without any northern flank, Joffre's forces would have been thinly spread, and not as strong as they were on the Marne in September, when French divisions outnumbered German 2 to 1. Admittedly, most of these scenarios would have relied upon a better system of command and control, specifically Moltke devolving command to army groups instead of trying to direct the operations of 7 armies on a individual/semi-individual basis. It would also depend on the Germans concentrating their cavalry divisions within the First and Second armies on the wing, instead of scattering them across the entire front.

Had the Germans and Austro-Hungarians followed up their efforts in 1915 by attacking the Russians in 1916, an end to the Eastern Front could have been achieved almost a year sooner. 1918 would be another point of departure; had the Germans kept better cavalry forces, and made these available in the West, and had clear objectives such as the rail centers at Amiens and Hazebrouck, the BEF could have been placed in an untenable position, cut from it's supplies and it's French allies.

As to a decisive battle for the Allies, the concept of decisive battle isn't exactly a useful one for the World Wars, considering how long they dragged on and how resilient the armies that fought them proved to be. That being said, the First Battle of the Marne could be considered decisive, as it ended German hopes of an early victory in France. Likewise, although not battles, the Somme and Brusilov Offensives might be considered decisive, with the latter striking a crippling to the Austro-Hungarian Empire and drawing Romania into the war, while the latter brought a halt to German offensive operations against the French Army, placing the strategic initiative in the hands of the Allied Powers. Of course it's easy for us to point out from well after the war, what it's decisive moments were. This would have been less clear to the actors involved.