1996 Ford F-150 Jump it, then it dies

I was driving and all the panel lights came on (check engine, ABS, etc.) Then they faded and went out, the radio turned off, then while looking for a parking spot the truck died and wouldn't turn over at all (no clicking or battery power). Got it towed home, it would jump then run for 45 seconds then lights would come on, radio would cut out, start running rough, then the truck would die again. Any thoughts? Could it be a bad alternator?