Don't abandon the battery just yet, although someone with more experience might be able to lead you better. I'm just going on what I've experienced with a similar situation. I found that a really really dead battery won't be able to jump start. One thing I learned from my dad is that you can take another car, hook the jumpers up and then run the good car at a "high" idle (200-400 rpms higher than normal idle) for about 3 mins or so. It helps to use the good car's alternator to recharge the dead battery some Before you crank it. After it sits and charges, try cranking the other car. If that doesn't work, take that battery out and recharge it if you have a 12v charger. Oh... almost forgot, if you have a voltmeter you can put that on the dead cars pos and neg posts and when you crank it, see what the voltage drops too.... again not a auto mechanic, I think anything lower than 9vs on a car and it can't start.
I don't want to lead you in the wrong direction, its just that your situation sounds just like one I ran into... with the dead battery that is. I had hooked up some new speakers and an amp to my radio. My radio is one that has a 5 min delay shut-off in it... you know turn car off don't open doors and it keeps playing. Well, I hooked up the wrong fuse size in the wrong fuse and my amp never turned off... draining my battery. Took me about a week to figure out why, but when the battery failed on me... I ran through the same kinda things.