Does it have differential?
What is the factory number off the back of the base?
To recap:
You are saying the machine drives fine in forward and reverse.
When you let up on the drive clutch and check the friction disk the friction disk does not touch the drive plate.
When you push the machine with the clutch not engaged and the engine not running you can't push the machine.
When you have the machine up on it's bucket, clutch not engaged, friction disk not touching the drive plate you can't turn the wheels.
Are all the above right?
When you turn the friction disk by hand what happens? Do the gears or chain move? Is the chain oiled? Are the links free, not binding and loose inbetween the gears?
Can you wiggle the gears no matter how slightly? Are they frozen solid or move at least 1/32 of an inch?
Something is wrong with the writeup. You can run in forward and reverse and evidently you can stop and idle so the drive clutch and friction disk moving properly and backing off the drive plate when the clutch is disengaged.
I oculd see a roll pin being caught by something but the axle would turn almost a revolution. Can you turin the wheels at all when the machine is up on it's bucket? At all, even 1/8th of an inch?