DIAGNOSIS The rotisserie motor drive gear is likely stripped. It's a common failure point under high load.
FIX Unplug the unit. Remove the back panel by taking out the screws. Locate the small white plastic motor assembly near the top. The gear on its shaft engages with a larger gear on the spit socket. Inspect the teeth on both. The small motor gear is the usual culprit. You must replace the entire motor assembly.
IF THAT DIDN'T WORK If the gears look intact, the motor itself may have burned out. You can test it for continuity with a multimeter. No continuity means a dead motor.
HEADS UP Ensure the spit forks are tightened securely onto the spit rod. A loose, wobbly load puts immediate strain on the plastic gears and causes this failure.