Great Uncle's Military Records

This is my great uncle, James Frank Dumas. Wasn't he a handsome man. Unfortunately he died very young at the age of 23 in 1946. He was on a ship that was sunk during WWII and he developed some kind of infection in his lungs from being in the water for so long. He died not too long after he came home from the war.
Several of my family members and me have been trying to find out what the name of the ship was that he was on. The people who are still alive when Frank came home from the service were so young that they don't remember much about his service in the Navy and they definitely don't know what the name of the ship was.

Through a researcher I found out about a website where they will look up peoples military records for you. I sent them all Frank's information and have waited for a couple months for the information. I received a phone call from the National Personnel Records Center, which is the website I mentioned earlier. The man on the phone told me that since my great uncle had been discharged from the Navy over 60 years ago his records are in the archives and it will cost me $65.00 for a copy of them! I was blown away! I told him I could not afford that and that really all I wanted to know was the name of the ship he was on that sunk during WWII. He couldn't tell me that information. I feel like I have hit a brick wall!

Does anyone out there know where I can find a list of ships and their crews that were sunk during WWII free of charge? Please let me know if you do! I would so greatly appreciate it!