Tines won't turn

Here are some possible causes and solutions:

Belt Issues: If the drive belt is broken or loose, the tines won't turn. Check the belt tension and replace the belt if necessary .
Idler Assembly: If the idler assembly is not properly tensioning the drive belt, the tines won't turn. Adjust the idler assembly or replace it if necessary .
Engagement Cable: If the engagement cable is loose or not tensioned properly, it may need to be tightened or replaced altogether .
Transmission Issues: If there is an issue with the transmission, such as a broken gear, the tines won't turn. Stop using the machine immediately and inspect the transmission .
Since you mentioned that your tiller tines were turning fast after replacing the carburetor and then stopped turning after connecting the throttle cable, it's possible that there is an issue with the engagement cable. You may want to check if it's properly tensioned and connected to ensure that it's not causing any issues How To Fix Tines That Will Not Move - Tiller Repair

Do you have the 2 speed or 4 speed version?

Do the drive wheels always turn when engaged?

Did you check drive shaft end play? Severe wear of the drive shaft sleeve, spacers, shims, and two drive gears can accumulate enough so as to allow the tine drive gear to displace far enough that it will no longer engage the large brass worm gear.

hAVE YOU TRIED ENGAGING THE DRIVE LEVER?

Transmission/differential.
Perhaps the unit sat for 4 years because the tines would not turn and your replacement engine has not solved the real problem.
I'd say disassemble the chain case to discover what's locking the tine drive.

check the shift linkage sometimes the pins fall out when you shift it does it move to freely

then you need to open the gear box and find out why if it has a forward and reverse the the shifting linkage it could be stuck in one gear and adding the other will lock it up as well

Yes, there are shear pins on the tines and on the wheels. Can you check to see if the belt actually moves when the pulleys turn?

I had similar problem recently with 2007 Huskee MTD series 410. The shift assembly bent and couldn't move the clutch collar all the way over on the drive shaft.

The tines are very close to the housing and sometimes you do get rocks hitting,as for the dirt it should have side panels to keep the dirt in place.

If you find one please let me know as I have the same tiller and no manual.