I checked the belt it seems okay. The blades engage. The motor runs. But the mower won't move forward nor backward.

There should be separate belts involved in movement and the mower deck... have you checked BOTH of them?

Is it a straight mechanical gearbox or hydraulic drive?

Hi,
Assuming the park brake is not locked; have you had a flat rear tire and lost the key in the axle on that side?
Peace,
Clarke