Jeep won't stay Running.

Hello I have a 2000 Jeep Grand Cherokee, my daughter was driving it in a
bad rain storm. She parked and then it would not start. Our first thought she
ran a puddle to fast wet something that needed to dry. We jumped her and
when we took our foot off the gas it stalled. We were able to get the car
home and took it over to advance auto parts whom told us that our two year
old battery was dead. We could not find the receipt and can not remember
where it was purchased to we purchased a new battery. Drove the car
around one day with everything fine and today we went to start the truck and
it did not want to start but once it did we were back to foot off the gas it died.
Suggestions do not want to take it to a garage and get hit with lots of dollars
to fix but can not let my young daughter drive a car that could break down. I
love my Jeep and need suggestions that I can understand. Help...