Help please 1992 Dodge Caravan, dead battery and...

Hi everyone I need help please.
about 3 weeks ago I was driving my car no probs, came home and parked it.
The next morning it wouldnt start...no dome light, no door locks, no
nothing. My dad came and jumped me a few days later and it seemed to be ok,
I even drove it to the store and back. But the next morning it was dead
again. Last Sunday my dad went and got me a new battery and put it in for
me, ran fine, went to the store, came back..next morning took my son to
school, did some errands and then that night I went to drive it...Monday
night it was dead. Is this an alternator problem?

Also I have another problem...Monday night I went to pop the hood using the
little latch inside the car and the cable broke and the hood never popped
open. Am I screwed?
Please help!
Rhonda