Hi,
I have the Mopho Desktop, not the Mopho Keys, so it may be different, but the manual I have says there is no complete factory reset, only a Globals reset - I'd have to load the factory sounds back in, to get it back to how it was originally.
Probably the most common reason for any sort of electronic equipment to fail or degrade with age is electrolytic capacitors leaking, or failing all together. Those are the can shaped ones. The largest ones on the board are the most likely suspects, but any you can see are candidates for replacement. In the case of the famous Casio DH-100 squeal problem, it's caused by a small 10uF can shaped electrolytic capacitor failing.
Leaking electrolyte can happen catastrophically (with a bang, or a puff of smoke), or just gradually, over time. Sometimes you can see they've leaked, and maybe see deposits on the end of the capacitor or the circuit board. Often, you can't.
You can try measuring them with a cheap capacitance meter, but measuring them in circuit won't necessarily tell you much - you may have to desolder at least one leg to get a measurement.
The value that the meter reads can actually be higher, for a failing capacitor, because it can start to conduct, which fools the meter. Bear in mind, that capacitor tolerances are allowed to be very high anyway - it might have been half the value marked on it from new, or at least 20% under, or it might have been 50% over.
The most reliable method is simply replacing all the electrolytic capacitors with one of the same value (in some cases its okay if it's a bit higher - e.g. for power supply smoothing), and at least the same voltage rating - if possible, go higher on the voltage rating so it will last longer. If you don't want to replace them all, start with the largest one, then check it again to see if you still have the problem.
Of course, you may want to find a repairer to look at it for you. I'm okay with repairing some things, but if it's expensive, or there's a lot to do, I'd consider taking it to someone else. I had all the capacitors replaced in the power supply of my Freeview TV recorder, not long ago. It had been getting more and more erratic over time, but that fixed it. If you can't find a synth repairer, an open minded TV repair man might be the way to go. They don't necessarily have to understand what they're fixing, to fix it. Capacitor replacement is one of the things they're used to doing.