A couple of years ago I bought a pristine WM-EX652 with box and accessories and to be fully operational it just needed a new belt. Replacing the belt is pretty easy but while working on it I discovered the weird solution Sony envisioned to save power: for all transport operations that requires high torque the belt is stretched, while during play the belt is kept relaxed to decrease the load on the motor. (sorry not my picture, grabbed on the net) that "power saving" is achieved moving the black wheel in the upper left corner in the direction of the arrow. And here comes the catch: when the walkman is off, the belt is kept stretched !. Last Sunday I did a bit of maintenance on all my walkman's and the 652 was the only one having problems playing a tape: after being kept for 1+ year in the stretched position, the belt would not give enough torque when in play in the "relaxed" position. The belt was new when installed (provided by Marian no less) and I could spot this potential problem the minute I understood how the belt stretching mechanism would operate ( and that is why I ordered immediately two belts). To me this is a clear case of Sony over-engineering: designing a transport with such a complex power saving strategy that, as a side effect, kills any belt pretty quickly. How on earth could such transport pass the QA process ? Anyway now the walkman is stored without the belt...
This mechanism is common in many EX series. I usually place battery in my walkmans and play them for few minutes periodically, probably it helps but removing the belt completely is the best solution.
Just a suggestion from someone who knows nothing about this model: is there any combination of button presses that releases the belt tension without creating another potential problem (such as having the pinch roller pressed against the capstan)? And if you then disconnect power does it stay in that mode? Simplest way to disconnect power is usually to put a plug (which isn't connected to anything) into the external supply socket.
Yes, it is possible to leave the walkman in the play position, but a pinch roller would press against its capstan creating a dent. The only long term storage solution is to remove the belt. The following generation of walkman's dropped that tape transport in favour of a more conventional fixed pulleys system. I have an EX672 and even with a simpler transport, the battery last even longer.
