1997 Pontiac Grand Prix Fuel pump or?

Engine Mechanical problem
1997 Pontiac Grand Prix 6 cyl Automatic 114000 miles

Hello,
I have been having problems with my car and no sure diagnosis yet.
1. The first sign something was wrong was when my car would not start. The key got locked in the ignition and my car had to be jumped before I could get it loose or the car would run.
2. The next day my car struggled to start, but eventually worked.
3. The next 2 days my car started up fine like nothing every happened.
4. The third day my car would not start again. The key would turn but the engine would not fire. It was jumped a few more times to get it to run.
5. Now, 9 times out of 10, when I start my car, it will die unless I keep my foot on the gas pedal and rev it up for several seconds. Sometimes when I do this, my car will start bouncing, but it will die if I do not do this. Sometimes the lights will dim.
6. I took it to a Pontiac dealership to get it checked out. They noted the car would start every time. They hooked it up to the machine and said they found it could be something w/ the fuel pump, and that when something hits in the right place, it would cause a no-start condition. (If you want me to get the exact wording, I can find the document and give you that). They told me they are 99% sure if they replaced the fuel pump, it would run, but what about that 1% they could be wrong?

-Could it be the fuel pump?
-Could it be bad gas?
-Any other ideas?

Thanks so much for your help - it is greatly appreciated!