Any idea what could make my engine light go and come back on?

I have a 2008 VW Jetta GLI. Its in pretty good condition. I just bout it in November, second owner. Its running smoothly. Anyway, about a month after I drove it, it started to not turn over right after fueling it. I would have to wait 5 to 10 minutes before the engine would start. This is around the time I noticed the engine light stayed on. This happened for 4 to 5 times in a row. I took it to Advance Auto to get a diagnostic test. It only showed a code for the gas cap. Even after tightening it, the engine light was still on. Eventually I decided to get them to test it again. This time the only code came up was fuel pump. I decided to see if it would help to put a fuel injector treatment in it. After a few days, the engine light went off, and I was able to start the car right after fueling without waiting. Now today, I am driving down the road and saw the engine light coming back on. And it won’t go off. I tried tighting the gas cap, etc. And its still on. Any ideas or experience?