First thing to check is the other threads about augers not turning since this is a common problem and comes up every so often. It also saves you time from waiting for someone to reply.
Since one of your augers is turning fine that means the whole auger system from the pulley on the engine forwards to the auger driveshaft is working fine.
The augers are attached to the auger drive shaft via shear bolts that go through holes in the auger axle and a matching hole in the auger drive shaft. Their purpose is to shear ( break) whenever the auger gets jammed with something such as a frozen newspaper, larger stick, rock, whatever. This protects the rest of the system from breaking, its better to replace a bolt than a gear case.
Before putting your hands into the auger area disconnect the spark plug, pull the ignition switch and move the throttle to "Off". I also put a 2x4 down the impeller chute.
When a bolt shears there may be a piece left in the auger driveshaft, you punch it out with a drift pin, centre punch or large nail. Do not replace the shear bolt with a regular bolt. You can buy shear bolts at lawn and garden places or generally anywhere that sells snowblowers. A local hardware might even have them.
Once you have made sure the old shear bolt(s) is out you need to use a grease gun and inject grease through the grease nipples on the auger axle. Then turn the axle a few time to distribute the grease. Do this a few more times so that there is plenty of grease between the axle and the drive shaft. This prevents the two from rusting together. Now put the bolt(s) in and tighten them up. The nuts are a desinged to be quite tight so that they won't vibrate off once they are tightened properly so they will feel kind of stiff when you are putting them on. I use a box wrench and a socket wrench to tighten mine.
If you need to move the driveshaft around so you can get a better angle on the bolt(s) you do the following:
- Take the 2x4 out;
- Engage the auger control
- Slowly pull the manual start cord, the driveshaft will slowly turn;
- Look inside to see where the bolt hole is.
- Repeat from step 2 until its where you want it.
- Out the 2x4 back in.