Regarding the Kenmore
There have been center dial Kenmores of more than one vintage, as I have two from 1970, but I'm assuming you mean a mid-70s to mid-80s machine? Even if not, like someone else said, a belt-drive is pretty much a belt-drive, though in my experience the earlier ones can be a little more finicky than newer ones (but that is just my experience only). The pre-1971 machines chew up belts much faster.
Here's what I do when I test one:
Visually inspect underneath through the service panel....if the belt is there, in one piece, and you can move it back and forth, that's good. If the motor is there and looks good, that's good as well. This is where you'll find a locked-up motor, pump or gearcase (or all three).
With the timer clearly set so the machine is OFF, plug the washer in. If you don't throw a breaker, you've passed the next test.
Put the timer in the last section of the final spin on the normal/cotton sturdy cycle, with the lid UP. Listen for any unusual sounds as the machine is basically in full idle.
Close the lid or depress the lid switch - the machine should spin. If you get that far, I wouldn't be too afraid of the machine, at least functionally/mechanically. Some machines have a dry agitate portion in the timer on the normal cycle, so you can test that as well, but that's hit or miss and depends on the model. It is usually in the final two minutes of wash. If your machine goes right from fill into neutral/pump out, it doesn't have it.
If your machine is a late model belt drive, chances are pretty good unless it has 500,000 miles on it that the belt is reasonably ok, at least to test with. I have not come across but one or two machines from the late 70s up that broke their belts, however they do wear over time.
Many late model belt-drives had leaky centerpost gaskets. If you see excessive rust on the baseplate, or better yet, a white detergent trail, this may be why the machine was parked.
I would not put any water in the machine yet until you have a better feeling that the machine can remove it on its own and that it is not going to spew everywhere. Once you know it MAY run and pump out, that's when I'd put water in it.
If you get that far and find nothing, you can cautiously say you may have found a jewel. Sometimes there's nothing wrong with a machine, or something that can be easily fixed or lived with as-is. The machine I most recently worked on revealed a dead-spot in the timer in the delicate cycle that could have been annoying to the previous owner, but I ran it seven cycles in Normal before I noticed it.
Good luck!
Gordon