I'm voting starter on this one. I had the EXACT same deal happen on my FJ62. Next time, take a hammer and tap on the starter. Dime to dollar bet it will turn over after you do that.
I don't trust Autozone or any other of those places as last time I asked them if they could get their hands on a driveshaft for a 69 Camaro and they asked if it was the front right or front left that I needed!!!!!