Craftsman Snowblower. One auger is disengaged...turns freely when touched....does not push snow

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this is easy job look at it , it will show you how it is done , just look good at it you do not need anything to do this couple of hand tools

You may it adjusted to tight.

Any chance it won't come up when you have the "drive" handle down ?? Newer snow blowers are often equipped with a "one hand" feature that will keep booth the auger and drive handles engaged (down) with only one being held.

the auger and impeller are geared to work together. the auger does turn much slower then the impeller. You may not have a problem at all

My 8 horse has an adjustment screw on the carburetor Turn it out a little at a time till it keeps running Just don't over do it If you turn out too far you will flood it.

Not sure how long you have owned this machine but the auger does not turn fast. It 's job is to chop up the snow and push it back to the impeller. The impeller is the round plate in back of the augers that actually throws the snow out the chute. That turns fast. Check to be sure the shear pins are not broken. Shut the machine off. Wait for the augers to stop spinning and then try to turn the augers by hand. If they spin on the shaft then the shear pins are broken-replace them by using original equipment shear pins.

I wonder if your cable has broken in half.

I am going to assume the belt is good if the impeller it running. You can check the belt by removing the plastic cover in the center of the snow blower.
With the unit safely turned off reach in and turn the blower by hand while putting a little resistance with your other hand on the impeller. Does the shaft from the impeller to the gear box turn?
Does the shaft that the augers are attached to turn? If the impeller shaft turns but the auger shaft doesn't, the gearbox in the front is bad and will have to be replaced.
I the auger shaft turns, check your shear pins again. Sometimes they will break but still stay stuck in the holes. Actually take one out and check it.
If it is a Craftsman you can get a manual from managemyhome.com and parts from searspartsdirect.com. You will need the model number of the snowblower. The number looks like 247.123456.
Any other questions please ask. Do't forget to rate this answer!

Check for another sheared shear pin.