Hi, Crash -While I don't have much info on the TC-650, I did get one once, which arrived with almost no packing material in the box... as a result the wood case looked like a mass of firewood splinters, and the chassis was kinda dented and bent; one circuit board was crushed, and broken, but almost everything else was intact. So basically having thrown out the metal chassis, I have most of the remains of the TC-650 carefully dismembered and sitting in a big 12" x 12" x 10" plastic bin.
As for checking parts that might have failed, I'd say check the Motor Run Caps; each of the three motors should have one, with the capstan motor - likely two, one for each speed. These are usually non-polar radial parts rated in AC Volts (rated like 4uF./250VAC) generally with a silver appearance, 2 or 3 terminals on the top and mounted in a clamp, if I recall correctly.
If the cap for the 3 3/4 ips speed is open or dryed out then the capstan motor may run only at the 7 1/2 ips speed, of course it could also be the switch is bad, or the motor winding for the slow speed is open, or something else entirely if a servo-control loop is used to drive the capstan motor's speed. I'm really not that familiar with the circuitry of the Sony sets, I can't even recall if I have the service manual on the TC-650, I think I do have the SM on the Sony TC-521, TC-558, TC-660, and TC-765, but they might be way different in their ways of driving the capstan motor, but I think those caps would be the first place to check - with an ESR Meter.
Wish I could help more, but I'm really not a Sony repair person.
-Steven L. Bender, Designer of Vintage Audio Equipment