2007 Crown Vic electrical problem

I have a 2007 Crown Vic Police Interceptor and recently the car has died on me twice in one week. I was driving one night and my cd deck shut off unexpectedly and also noticed my odometer wasnt showing any more. I looked at my head lights they were really dim so i pulled into a parking lot and the car was loseing power in which i shut the car off. I tried to start it again but there was nothing. So i had a friend come and give me a jump and it started and drove it home. Well 2 days later i was driving to my sisters house and all the power issues started to happen again, so i kept driving thinking i could make it there but the headlights completly went out so i had to pull over. my sis came out with her car gave it a jump but the battery wasnt keeping a charge. It also said i was low on fuel which i know this wasnt right cause i just put gas in it. So as of now i put a new battery in it and got the old one tested and it said the battery was bad. I am seein if anybody has had this problem before and if so is there anything else i should check

alternator?

The altenator checked out good. im waiting to see if anything happens since ive changed the battery.