intrepid is possesed

Hi I have a 96 intrepid sat for a while and was dead when I went to start it.so I give it a boost and it starts but the radio, pwr window's, pwr locks, and all the lights where going crazy. then after a minute it dies. so I unhook and clean the battery and cables give it another boost this time it starts without acting all crazy but as soon as I unhook the booster cables it die's .. not sure do you think its the battery or the alternator...any help would be great thank's.

Since the car was already started and running, would suspect alternator.

These cars need all three of these: a good battery, a good alternator, and clean connections.
Start there.....