2004 Chevrolet Cavalier Won't start

I have a 2004 Chevy Cavalier that I recently purchased. It ran great when I bought it from a private party, started it up several times a week, moved it around but did not get it on the road. I did this for several weeks and it was fine. Suddenly one day I tried to start it, it started and immediately shut off. I was confused and tried it again, wouldn't start. After checking to be sure the battery was fully charged and adding gas (although it showed 1/4 of a tank) still couldn't get it to start. I tried the other week hoping it would start but didn't. I noticed during my last attempt that it shows 1/2 a tank of gas until I turn the switch to start it. As soon as the engine starts to crank the fuel gauge immediately bottoms out. Let off the switch and it goes back up to half a tank. The previous owner had recently replaced the fuel pump so I'm not sure what it could be and I have no way of getting my car to a garage at the present time. If you know what the problem is could it be fixed/replaced at home? Thank you!