It won't start at all.
If I get a jump, it starts up
then dies after I disconnect the jumper cables.

Try leaving the jumper cables connected for a few minutes before trying to jump start the car. I have seen cases where the battery has become so weak it has no power at all to even produce the spark necessary for the plugs to fire. Leaving the cables connected for a few minutes will allow the other cars alternator to slightly recharge your battery before attempting to start it. It goes without saying to use good jumper cables. Cheap ones will get too hot too soon. If that doesn't work, my next step would be to take the battery out of the car and try charging it form an external source, or switch the battery out with a known good one from another car or a new battery.

Mike

The battery provides the initial fire to crank and start your engine. Once it starts though, the alternator takes over and runs the car as well as provide a trickle charge back to the battery to keep it up. It sounds like your alternator is bad. Once it quits on you, the car will run off the battery until you drain it. This would account for the vehicle starting and then dying once the cables are removed. I would pull the alternator and take it to parts store (Kragen, Autozone) and have them test the alternator. If it checks bad, replace and then jump your vehicle and let it run to build the charge in the battery. If the battery doesn't seem to hold the charge it may be that you ran it dry. Pull the battery, and take it to the parts store and have it checked. Make sure your alternator or serpentine belt are in good order and that the tensioner is providing the necessary tension to fully spin the alternator. Beyond these items, you may have a fault in the wiring system but not likely. Typically, it is the alternator in your situation.