Overheated, blown battery

30 miles after a new alternator and battery were installed in my 2000 one ton pickup, I drove it just 4 miles when it lost power and started to die, I pulled off the road, then the starter engaged (I may have tried to restart it) and stayed engaged with the key off and removed. All fan belts, air conditioning belts running. Battery too hot to touch. Had to remove starter relay, lights still on, removed fuses, disconnected battery, but acid dripping from below. Could a new faulty alternator cause that? The mechanic who had put in the new alternative and battery just the day before this happened, thinks the starter is the problem.