Snowblower drive problems

Hello all, I have an MTD snowblower model 31A-CAD729.. it just doesn't self propel. I've checked everything from cables, skid shoes, new drive and auger belts... watched dozens of videos...it doesn't appear to have a standard drive disc design... Anyone familiar with this machine... your help is appreciated

That is the correct model number...and yes it does have the plastic transmission. That's another reason I became so frustrated... I could never locate anything on the internet to match this model.... Thank you very much. Your response is greatly appreciated.

You're missing a digit in the model number. It should be 31A-3CAD729 which is a 2006-7 model.
 
Probably has the General Transmissions HR300P unit. External parts are available but not the internals.

The image of transmission is not the HR300P so I don't who makes that one but is definitely a plastic housing.
 
Now you where shops are having problems doing repairs as costs are so close to replacement costs sometimes.
 
I got a 86 Suzuki 230 in the shop now that is only worth 500 once repaired but is needing that much in parts alone. That going to be the customer's call if it the work gets done.