WONT IDLE STUPID QUESTION

Ok I started my jeep today and the damn thing could barley run.
Infact it would die once in a while too. I noticed i left my dome light on so i figuered i needed to run it a bit too charge my optimia yellow top.
Well to keep it running while i ran into the house i turned the a/c on.
After my half hour drive to work, it still just dies. Is it my battery not keeping a charge? Alternator bad?!!!1

Check all your cables making sure they are corrosion free & tight! If that is not it have your alternator & battery checked at your local auto store.