Auger clutch cable breaks at hook

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It sounds like the auger always turning is the auger engagement handle/line/connections are not adjusted correctly. They/it is too tight causing the auger to engage before it should. It may be up at the handle where you loosen a jam nut, screw in or out a threaded shaft, and retighten the jam nut. (If you have ever adjusted a bicycle brake it is similar.) (I have a craftsman, made by MTD, and I think I saw MTD also list Ariens.) Or it could be an adjustment somewhere else (but I'm not sure where).

As far as one auger moving and the other not, you may have a shear-pin (shear bolt as the manual calls them) on each side of the auger's shaft (my craftsman has one on each side), and the one on the side that stops turning is sheared off. (It moves without snow present due to the driveshaft inside the outer auger shaft turning, but it won't turn under load (snow).) You may confirm a sheared-pin by turning the machine off and try to turn the auger blade. If it turns somewhat easily, that's a bad shear pin. Remove the old shear pin. If the old one is as long as the new one, that aint the problem. The shear pin in the image is one kind. Mine appear as a straight bolt (no grooves), threaded the entire length. You will have to rotate the auger blade until it aligns with the hole in the shaft. Use a nail that fits and rotate the blade until the nail goes in. Remove the nail and screw in the shear bolt:


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The auger clutch control up at the handle looks like this:
From my manual
Auger Control

• To check the adjustment of the auger control, push forward the left hand clutch grip until the rubber bumper is compressed. There should be slack in the clutch cable.
• Release the clutch grip. The cable should be straight. Make certain you can depress the auger control grip against the left handle completely.
• If adjustment is necessary, loosen the hex jam nut and thread the cable in (for less slack) or out (for more slack). Recheck adjustment. Tighten the jam nut when correct adjustment is reached.

Here's another view of that:

I hope the above info helps you take care of both issues.

You may it adjusted to tight.

I wonder if your cable has broken in half.

I assume the cable to the auger was removed and needs to be re-installed.
There should be a clamp that the cable ran thru, then attaches to the auger
control. Find this clamp on your snowblower, and route it thru this clamp
then attach it to your auger control.

If I was you I would check key way to see if it has sheered off. It is in center of big drive pulley where belt goes on, Just remove nut and slide pulley off to check condition. Best to split snowblower in half. Your snowblower has two main pieces it will be 4 or 6 bolts to separate your machine.

If the blower (impeller) turns and the auger doesn't there is a 90% chance you broke the shear bolts that protect the auger gear box.

Look at your auger and you will find the bolts shown at the arrows in this picture are missing. Some snowthrowers will have two bolts and others like the new Craftsman will have four.
You can get new ones at your local mower repair shop, your local Sears mall store, or online at sears.com.
Use shear pins or shear bolts not regular bolts. The shear bolts are designed to break off so you don't tear out the front gear box.
Feel free to ask any other questions. Don't forget to rate this answer!

the augers on many craftsman snowblowers have a sheer bolt. If the auger encounters too much resistance, ie, a foreign object like a piece of wood or even a newspaper buried in the snow, this bolt will break off preventing damage to the gear box, which is a lot more expensive to repair than replacing the bolt.
This bolt requires not tools to install, just insert and secure with a cotter pin.
The parts dept at sears can sell you the replacement bolts with the correct sheer force rating. Have your snow blower model number handy when you call or go in.

my auger cable is not working the auger so i adjusted it and it was to tight and the plastic holder that holds the cables poped off and broke,now the cable i adjust it and nothing happens,cable is all hooked up and seems ok but it will not work right,but the auger spins with out the cable,wondering if it needs a new auger cable

my auger and impeller froze too. fixed by clearing all snow, ice,stone build up behind impeller it works fine now.. hope that helps