> without ripping the whole unit apart?
Well, what you gonna do? A capstan-less tape deck is little value, basically electronic waste.
I never met this model. However the image sure look like the early TEACs. These (I know too well), the top/back cover comes off with 6 or 8 screws. Great access with little fiddling. Capstan motor butt will be right there. Wires may be visible. With luck you may be able to probe the power switch and what looks like a tape-break switch.
The partial manual I found shows two versions, single wall voltage and jumperable wall voltage. Since you think the rest of it is OK, I would assume the jumper is not the problem. Here's part of the schematic with the capstan path highlighted. S1 must work, FT is probably OK. S15-1 must be tape-break. S14 sets 50/60Hz; I would expect it to run but poorly if this is wrong. S8 is speed-switching (the motor is 4/8 pole). The rectangles on the switches are just arc-reducers.
Please do not get killed in here!!
From black wall-cord lead you should have 120VAC to tape-break switch. With tape-not-broke you should have 120 on the other side of tape-break switch; also to the white wires on the reel motors. Also at the tape-speed switches.
The large caps on the 50/60Hz could fail. 250V rating is a little slim to my eye. These are MOTOR Caps, not audio caps. Shop for "Motor Run" caps (start caps are different).