Car dies after being jumped?

I was driving across town last night and the lights inside the car ( gas gauge, speedometer, radio lights) got really dim. I came start home and pulled in the driveway and turned the car off. When I went to start it again it wouldn't start. The headlights and inside lights still worked but the radio reset itself. I waited until the next morning and got a jump. It's started right away I let it run for a few mins and when I went to put it in drive it died again. It's a 1996 ford escort lx. When I go to rev up the engine while it's park the RPM is not working. I put another battery in it and its still not working correctly. Could this be the alternator, battery, ignition coil. Any idea's? I'm a single mom with three kids so I'm hoping it's not an expensive fix.

Sounds like an alternator problem. The part is not that expensive, however it's a 1.5 hr to 2hr job.

Alternator needs to be replaced is what it sounds like to me. Take it to autozone and have them check it for free.