Riding Mower Won't Start?

I have a 18.5 hp Craftsman mower. The engine won't turn over. I'm reading 12.4 volts at the starter when I turn on the switch, so I believe the wires, switches, ground, and solenoid are all good. I removed and tested the starter. The starter spins when I wire it to the battery, so I believe the starter is good. With the starter installed and the ignition on, the starter gear will engage with the motor, but won't turn the motor. Could the motor be frozen? Could the starter still be bad where it spins when not installed, but is unable to turn the motor when engaged?