'98 Chevy Blazer dies when accelerating

I purchased a used '98 Blazer with 94,000 miles and a V6 engine. Yesterday after stopping and beginning to accelerate again (such as at the bank, red lights, and even when going uphills) it would die. It didn't sputter or anything, it just turned off as if I had turned off the key. I'd have to pull off on the side of the road and start it up again. It would always start, but sometimes it took several cranks before it would start. The battery light was coming on when it turned off, but we checked the battery and alternator and both were fine. HELP!