2005 Pontiac sunfire wont start,

I have the exact same problem, including shimmying and car dying. I can add this: NO CHECK ENGINE CODES FOUND! The car would not restart, but after resting for about 20 minutes would fire, sputter, and die. The last time this happened it was an ignition control module, which are known to go around 110,000 mark, and they usually take the coil pack with them. However, this time I suspect the fuel pump for a myriad of reasons. Mostly, because the car is 130k miles in, and this is the kind of thing that goes around that time.

Well, you may have shot yourself in the foot by cranking the engine until you totally killed the battery. If there were any fault codes in the computer that could lead you to the cause of your engine not running, they are probably gone now, so the car will have to be diagnosed manually.

When engines stop running, they almost ALWAYS do it suddenly without any warning - so you are not alone. The problem here is that there are probably at least 300 different parts of your car that can be the cause of this. So, I am not surprized that you have been told that it COULD be so many different things. The fact-of-the-matter is that NOBODY can tell you with any certainty what is going on with your car without FIRST performing some diagnostics to eliminate certain possibilities.

The only way any of that is going to happen with any efficiency, is to get the battery charged back up first. NOTHING on your car works properly with a discharged battery. Only after the battery is charged can the other systems be tested.