Preface: My expertise is in military small arms, but I will do my best to give you a quality answer.

PT boats as used in WWII, originated in concept from W. Albert Hickman's designs at the onset of WWI. The US Navy began real interest in the late 1930s, with four companies, Huckins, Higgins, Elco, and Philadelphia Naval Yard submitting prototypes for testing.

Construction began in 1941, for the Elco 80', Higgins 78', and Huckins 78' designs. All had various layouts and differences in construction methods, Lindsay Lord's Naval Architecture of Planing Hulls would be a good source of more information on that. PT 109 in particular was an 80' Elco design.

Now to the meat of your question: the majority of PT boats were in service from 1941 until the end of the war in 1945. A lot of the boats were scrapped since the cost to maintain (wood hulls) and run them (their three massive packard engines burned high octane aviation fuel) was considered too much for a now peacetime navy.

There are 12 known surviving examples in the US, some were converted to use in the civilian market, and no longer resemble thier wartime condition.

The best surviving and restored example of an Elco 80' is PT-716 located at Battleship Cove Museum in Massachusetts.

There is also a 78 foot Higgins type boat in San Francisco that is restored to wartime specifications, and is in the water and operational. I was able to see this one in person.

A lot of my knowledge comes from when I also built a model of PT 109, and went to the local library for more information. I will admit to not rembering specific texts or authors for each peice of information, but the data from the National WWII Museum archives as well as the Museum of the Pacific War helped me remember.

I hope this helps answer your question, I apologize for any formatting mistakes, I am on mobile. Moderators, please let me know if this is up to par.