check engine light and incorrect fuel reading

Sorry if someone has this same question posted, didn't find anything that was close to my issue.

I just bought a 2005 Malibu Ls. Last friday after i filled the car up with gas the fuel gauge said my tank was empty. I check the gas cap and it was tight. After driving for about ten min it worked fine since. Now today i drove the car for a little while and everything was fine. My wife was taking the car to visit someone and the car wouldn't turn over, you could hear it trying to but all you heard was a clicking noise. The car did start after a few minutes and then shortly after that the fuel gauge read empty and the "check engine light" now came on. The dealership said it sounds like its related to the battery or that the battery isn't charging. Does anyone else have any idea or heard of this problem??

Thanks in advance!