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Just so you can compare, your belt part number is XXXXX (MA) or it will be listed as a 1/2 inch by 35 inches long.
You can adjust the idler pulley as well as the cable. You will see a bolt in the middle of it. Loosen this and the pulley will slide towards the belt about an inch. Re tighten the bolt and see if that gets your belt tight
Make sure that the belt is not wrapped over a belt guide or brake, also make sure the idler pulley is on the outside right of the belt, not inside the belt. Your gear box sounds like it is working perfectly. The impeller spins about 5 times faster then the augers.
This has got to be something simple. Trace the belt around the pulleys with your fingers like you have never worked on anything before, the auger turning slowly indicates that the belt has some tension on it (it should not) when the handle is not depressed.
Can you push the pulley further to increase pressure on the belt?
Ariens had a model that you could not over tighten the idler pulley. It could be something like that (it had to do with pivot points) you may consider bringing the pulley back about half of the adjustment to see if that helps
UPDATE- When I got home from work, I put the snowblower to work. It seems like the auger just tosses the snow around inside the housing and doesn't want to send it to the chute. The impeller pins are intact and nothing in the gear case is wrong. Could I have the auger blades on wrong? Are they particular to left and right? If so, this would make sense as the blades may not be turning the right direction and thus only tossing the snow around instead of feeding it to the impellar. Can you verify the correct orientation of the blades for me? Thanks.
Sorry for the late reply. One blizzard in Mass and I get to plow for almost 18 hours!
Yes the augers are most definitely right and left. I have done this before (reversed them) and it is very frustrating. There is no way to tell you which auger goes on which side, you have to look at them and visualize which way they turn. They scoop snow into the auger housing and should be pushing it towards the middle instead of out to the sides. The easiest way is to look at another snowblower and compare them. They all look the same and turn the same direction.
Here is a breakdown of your auger assembly, maybe it will help.