Typical capstan repair process
A common defect affecting these machines is the "runaway capstan" problem, where it makes loud whirring noise and runs at much higher speed than normal.
In most cases the fix is to replace electrolytic capacitors C5, C7, C9, C13, C15, and the ceramic C2 to get it back to normal. Once it's working, use speed calibration process from the service manual. Also check the voltage on the cathode of the zener (under C15 in the picture below, right-hand lead) to be about 9V.
If replacing the capacitors listed above does not resolve the issue, that probably means that one of the traces has corroded and disconnected. Check continuity of all traces on the board with an ohmmeter on a high setting, in particular to the left of the center hole. You can also compare signals at the ends of traces with an oscilloscope while it's running. I've seen two cases where the trace between C7 and R4 has corroded right at the edge of the pad of C7, one case with the trace between IC1 and C16, on the edge of IC1 pad, and one case with the ground bus between C7 and the zener.
After repair I recommend using flux remover to wash off flux residue to reduce the chance of further trace corrosion.