There are a few possibilities:
(1) That some components on the circuit board have failed or gone out of spec. This may be fixable provided you can find a service manual and equivalents.
(2) That the platter system is damaged. The Sony X7 had a series of magnetized markings on platter's outer edge which are "read" by a tape head. The tape head feeds that info to the speed circuitry. If the markings are obscured or damaged, or the tape head is gunked up, it may not be sending proper readings. CAREFULLY examine and perhaps clean both.
(3) Like any motor, the Sony's needs some lubrication. Find a service manual and see if you can clean out the old stuff, what to replace it with and where the lubrication needs to go. Bearings can get damaged too.
The X7 was a very good (if butt ugly) table. It's worth fixing if you can do it for under, say, $200.
I think -- but can't guarantee -- that the only real difference between the X6 and X7 was the tonearm. You can probably pick up an X6 as a parts unit fairly cheaply and use it as an organ donor if necessary.