You can try to see if it is the YM2610, by taking a can of compressed air, turning it upside down, and spraying the cold liquid onto the chip. The cooling down of the chip might be able to get it to work normally again, if it is truly a case of it failing due to getting too hot.
As for replacement ICs, Chinese eBay sellers sell YM2610s for $2 each or so, with free slow boat shipping. No idea if they're any good, but it's cheap enough to risk it I suppose. If you do replace it, I'd highly recommend installing a socket first. This will make it much easier to replace the chip, should the replacement be bad, or ever go bad.