This might be a noobie question, but my battery is dead, my car hardly turns on, but when my key is on the on position the battery light comes on, but if I somehow turn the car on and its actually running it turns off. So my question isn't the battery light supposed to stay on since my battery is bad?

 

Battery warning light will stay on if there is an issue with the charging system and not when the battery is bad or not fully charged. I'd borrow a good battery just to test. If it starts normally, get a new battery.

 

If your car shuts off after a jump start, and can not run on its own, you alternator is not working.

 

The battery starts the car but once it's started the alternator takes over and keeps the car running. Take your battery to an auto parts store and get them to check it for you. Chances are it's done for and you'll have to buy a new one