How do I adjust the chute on the cub cadet snow blower it only goes partway to one side and all the way on the other side

Here for parts diagrams;

https://www.cubcadet-parts-direct.com/Cub-Cadet/DrillDown/4285-297/551-45

flexible wire outer case , bend the case and allow wd-40 to penetrate to the steel wire inside
plastic covered
allow the wd-40 to dun down the wire all the way throufg
replace the cables

more than likely a carb issue. Cheapest first fix is to drain the gas refill add one half can of Sea Foam and see if that resolves it.

The simple solution is the replaceable shear pins in the front auger have sheared. This is normal and protects the snow blower from major repairs. I suggest going to youtube and search "replace shear pins on Cub Cadet snow blower." There are a dozen videos that will help you troubleshoot and make the repair.

The cable from the speed selector to the back of the snow blower frame needs to be adjusted. Instructions are in any Tory-Bilt, Craftsman or Cub Cadet owners manual.

(32 degrees and above, 30w oil) - (32 degrees to 0 degrees, 10w-30) - (32 degrees to -20 degrees below 0 and beyond -20, 5w-20 or 5w-30) Cub Cadets call for a low ash oil. it can be purchased at any cub cadet tractor dealership.

YES A NEW LIGHT CAN BE INSTALLED BE SURE THE LIGHT THAT YOU PLACE ON THE SNOWBLOWER HAS THE SAME AMPS FOR THE LIGHT

cable or chute frozen
if cable is good loosen bolt on the side to give it alittle more play

That looks like a Cub Cadet part # for the Snow Blower.
You will absolutely need to customize a Belly bracket and Mule drive. Possibly find a Cub Cadet belly bracket and modify it to match your mounting points on the TY4000

Clean your carb, if you have not stored it correctly you have a dirty carb now. Carb could be gummed up.