98 Chevy Blazer (auto w/78000 miles)

We had 2 cracked heads and had it repaired, soon after getting the car back the ac stopped blowing cold air and the battery was dead. Could the ac be the reason the battery is dead. We've bought 2 batteries and both have died within 2 weeks.( We've checked the alternator ) the mechanic thinks it might be an electrical problem.
please help.