Why won't the tines turn - Ardisam Inc Earthquake Mini Cultivator

Two possibilities. Something has jammed the tines.
Pull the spark plug wire off and tuck it away someplace so as not to touch the plug.
Tip the tiller up and examine the tines for obstacle such as a rock. If there is nothing jammed try to turn the tines by hand. If the they turn freely you most likely broke a shear pin that secures the tines to the axle.Clean the axle and tines and examine very closely for the pin.
If sheared ( broken) you will need to drive the broken piece out and replace the pin.
There may also be a problem in the transmission case. You would need to remove the tines and case to open it

Either clutch is bad or teeth are striped in bottom gear box. remove tines run engine and see if you can feel movment in lower gear box, if yes the gears are gone. If no remove engine to expose clutch.

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.

Detatch the HEAD and rotate it and then install it. There is a good chance you have Jammed the Head and this should reduce the pressure and allow it to work.

remove the spark plug and pull it to force any fuel and oil from the cylinder hold a rag over the top of the spark plug hole as fuel and oil will spray out check the oil level before running the engine again

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

Sounds like a depth adjustment or a leverage problem.
Check your manual to see if you are able to lower the tines to a deeper position.
There usually is also a handle adjustment to raise the handle to get more leverage. (Not all Models) By pulling back on the handle it forces the tines into the soil and raises the tires. This allows the tines to agitate and do the work while at the same time walking the machine forward. When you push up on the handle the rubber tires provide traction and forward movement and less digging on the tines.
Method: Possibly by allowing a little space between passes your wheels won't hang up in the previous dead furrow. You can then go back over the skipped spaces or cultivate from the other direction and a criss cross pattern.
Best wishes,
TF

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?

SOUNS LIKE SOME THING CAME LOOSE IN SIDE THE TRANS

Mine did the same thing....two things to check: 1) air cleaner, make sure that it is clean 2). gas filter in the gas tank. Take a short piece of wire and fish the black line out. On the end is a small fuel filter. After I flushed mine fuel filter out it ran fine.

Mark