John,
Know what you mean. Been there, done that, got the T-Shirt
I found that when this happened, I found that if I turned off the ignition and tried again it would work. I would have the dash fan on low, if it started blowing all was well, if not, tried it until it did work. Sometimes took two or three tries. Replaced the batteries two years ago and haven't had the problem since. (knock on wood!!) BTW, it also effected the windshield wipers too.