Were the augers ever removed? Are they locked to the shaft? What is this machine?

The augers have never been removed and they are not locked. It's a Montgomery Ward/Gilson snowblower.

IF they aren't locked to the shaft, what would you expect?
Look for shear pin(s) that have "sheared".

As Bill mentioned, the augers each are secured to the shaft. If they are not, that's a problem. If they are locked to the shaft, but the shaft turns freely, that's a bigger problem- like a worn gear in the front box. You can see if they move independently from one another.

Does this model have a v-belt on it?, Maybe though it's not broke it could be stretched and as soon as a load is put on it, it is just slipping, & not tight enough to turn your augers.
Just a thought