Hi Chris,
Welcome to the forum.
First, I suggest you download the service manuals since fixing this problem is bound to require opening up the machine and working on the guts.
If you check out the stickies located above the General forum, there are links to just about every Otari 5050 service manual for download.
I would guess that the basic problem is that the take up reel brake is not disengaging. It could be that the brake band and rotor are stuck together and just need to be pulled apart and cleaned or it could be an adjustment thats really out of whack.
Most of the time, these kinds of problems become obvious once you get a close look.
Of course, it could also be the motor or control electronics. Finding out if the motor is getting juice would be a good place to start if you rule out the brakes, frozen bearings or mechanical obstructions.