Senior Member
Join Date: Aug 2007
Location: Northampton, MA
Posts: 956
Bikes: Iron Monkey: a junkyard steel 26" slick-tired city bike. Grey Fox: A Trek 7x00 frame, painted, with everything built, from spokes up. Jet Jaguar: A 92 Cannondale R900 frame, powder coated matte black with red and aluminum highlights.
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Yeah, seriously, thrift store bike. Find one with the same number of gears in the back. If the new bike is a worse bike than your old one, just swap the back wheel.
I agree with everyone else here: either the bearings are gone, the axle is broken, or both. Once you've solved the problem, take a look in there and see what you can see about how it works. It's too bad that this is one of those hard-to-solve problems. That's a tough way to start learning about how bikes work.
It's awesome that you posted these videos, by the way. Very, very helpful.