I found this old post on the forum. He was also having issues starting his car, similar to you. It sounds very close to your issues and is probably worth looking at. I mentioned it in an above comment, but when I was researching it a lot of people found an issue to be with the fuse box. A bad connection would definitely count as a problem that could flare up, especially for a car that was in a serious accident.
Like I've said before, these are all guesses based off what I've found online. Checking a possible bad connection is a lot more inexpensive than a new fuel pump though.
fuel pump problem
i had the same issue, couldnt hear the pump when key was turned to on position.
FINALLY FOUND THE PROBLEM AFTER 6 MONTHS OF FRUSTRATING STARTS AND MONEY WASTED!
its the connection between the fuel pump to the relay behind the rear fusebox.
I pushed the connection (wire harness) together to the back of the fusebox where the fuel pump relay is located on the fusebox. seems to be a misconnection that won't allow the power to reach the fuel pump.
still havent fixed it properly but atleast i know where the problem is located.
hope it helped you guys somehow...
For fuel pump brands, there's not a lot of options. I always go with ACDelco when I can for parts on my G6, unless there's a massive price difference. They specifically deal with GM, so it's a good match. I checked AutoZone's website and it was like $400 for ACDelco and $250 for Delphi and Spectra, so I'd likely use either Delphi or Spectra.
I did see a recall for fuel pumps purchased for G6's between June 10, 2013 and Aug. 16, 2013. I really doubt that's the problem since that's such a brief time frame for a specific dealer. Worth mentioning, just in case.
Fuel Pump Safety Recall: NHTSA Campaign Number: 13E-043
Personally, I'd check out the connections in the fuse box and see if something's loose first. I don't have my manual handy, but it'll be in yours under fuses in the index. The fuse boxes are located on the driver side in the engine, the driver side of the trunk and the passenger side towards the middle of the car.