Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
Your assumption could be correct. Capacitors are temperature sensitive. Using a board that is below 50 degrees F., unless it is unusually tough, or intended for outdoor use in fairly cold temperatures (the way circuitry in digital cameras and in rangefinders and binoculars tend to be made) it can be damaged.
Any or all large capacitors could be damaged. Look for any that are burst or leaking, or whose tops are bulging... though I doubt you'll find any such, since that's more of a high-temperature failure mode.
The audio amplifier section definitely has a damaged component in it. It may be also that the power regulation or power distribution has a bad part in it, if a diminution of voltage level from the power supply resulted in weakening of the audio output - as it well might, so a capacitor failing in the power supply could well be the primary fault in this case, not just capacitors everywhere and in general.
A way to tell if a capacitor in the power supply has gone bad, would be to see if excessive ripple voltage, AC voltage essentially, exists on the power supply output (internally to the whole Yamaha device. Or externally too perhaps, if it has an external AC Adapter.)
Yes, your keyboard uses DC for its circuitry, for sure.
I unfortunately don't know circuit board conformation specifics for this model. Test point information and values in specific could be found in a service manual for this model or for this model series.
The service manual for this model line can be had from this page, with some patience, free of charge:
After bringing up that page, you have to wait about 20 or 30 seconds, then scroll down to below the preview image, and click on the link, rather small and inconspicuous, that reads (by that time, but not at first)