1993 Corsica starts only when jumped

My Corsica runs great but needs to be jumped in order to start. The car stays running but when turned off it doesn't start back up. I put the battery in another one of my cars and it started. but when I put it back in the Corsica nothing. Can you help me Please I don't want to go out and buy a bunch of things if it can be narrowed down to something.

Might be a bad connection on the battery cable. Make sure theres no corrosion under the boot of the cables. When you put the battery in the other car did it start fast or did it chug for a few seconds and then start? If you open the door of the corsica, and look at the dome light, is the light bright? Or is it kinda yellowish brown?