A little more info would help.
For example, is this a machine that you've recently acquired and you've never seen it work, or was it working fine until this happened. The beaters are driven by a worm gear, so I wouldn't expect you to be able to rotate them by hand easily, but since I don't have one of these to play with yet I can't be sure. I can tell you that the beaters on my Mixmaster Junior(also driven by a worm gear)are very hard to turn by hand, and that's if you can get them to move at all. It's probably a bad idea to do it anyways.
Now that that's out of the way, the model 10 disassembles pretty easily for inspection, cleaning and lube, so I wouldn't hesitate to investigate this. Better safe than sorry.