I got into my car today tried to start it accessories came on radio came on but nothing but dead silence. There was clicking. Then when it finally does start it barely runs gave it gas it stalled out battery light came on assuming it's the ALTERNATOR.

 

Alt or battery.....the accesories don't need the power that the starter does that is why they worked and the starter didn't.

Jump run for a while.....then test later. If it doesn't work or you get this problem again check to make sure all lights are shutting off.....i.e. trunk light. ANd then if it the all are off. It is your alt or your battery is too old.