I don't believe its just an issue with midi. If its one of those digital rom sound oberhiems open it up.
First check to see if the power supply is giving the board the right voltages. It should be sending 5, 12, 15 volts, one of those numbers. The voltage regulators will correspond with being 7805, 7812, 7815. etc.
Make sure the five volt section is working well and giving you five volts. If it isn't, fix the power supply, then try working the machine. Also go ahead and replace that battery with a new one.
If it still doesn't work and you see great big square chips with what looks like hundreds of little legs on them, you are screwed. If you see rectangular chips with legs numbering in the twenties, you might have a chance of finding and replacing the bad ones.
But i'll make a prediction here and now that the former is the case and your box is dead.