02 Tribute No Power Misfires Galore

My daughter's friend from college just limped into town in an 02 Tribute desperately needing help. My back is up against a wall since it is exam week and I don't have long to get this thing running. Here's the deal: the vehicle has no power and is misfiring on 4 of the 6 cylinders. However, when I let it sit for a while and started it back up and drove it, it ran fine for about 15 minutes, at which time I kicked it into overdrive on a long straightaway...bad move. The car almost shut down and wouldn't go up even the smallest hill after that. When I put it in neutral and floored the accelerator, it would only get to 2200 rpm. Now it's running rough. The girl says it's been getting worse over a few months. At the same time, she says she is having to jump the battery a lot. Any relationship between these seemingly unrelated problems?

Normally, I'd just replace the coils on the individual cylinders, but I have 4 cylinders misfiring and these things are $65 each. Before I run down that path, does that sound like the issue? Are there other things that cause misfires -- vacuum leaks, camshaft sensor, crank position sensor, etc.?

I think this problem was resolved, see Ford escape.

http://www.automotiveforums.com/vbulletin/showthread.php?t=972629