I have had this EXACT same problem on two 70s-80s GM mechanical (I mean not LCD) clocks, and many related problems in others. The way the clocks are designed is the motor drives a gear, which drives a gear, which drives another gear, which turns the mechanism. The knob that sets the clock is another gear off the side of the mechanism. When you pull on it, it lines up with the clock gears, and you can turn the clock hands! However these are just plastic gears.
And what happens is people will pull hard on that knob, and break the teeth off some of those gears, because they don't let it line up. They just pull too fast and too hard. The teeth not only get messed up on the setting knob, but also on the clock gears too. So even when you aren't trying to set the clock, the broken gears are turning along with the clock. Well because these gears have broken teeth, they jam up the clock, and it doesn't turn. The motor will continue to run, while the gears just keep "trying" but nothing happens. Some tell-tale signs are dust/powder shavings in the clock body because the gears are shearing, and if you see "ghost" movements of hands or hand "bouncing." Even if the clock is just off time, this is because those gears are probably turning fewer revolutions than they should.
This is very common on these GM clocks, and both the replacements I got from the junk yard were this way. But try eBay, or one from a car you know works.
Good luck!
Greg
