Sounds like you have a broken lead to the synth engine proper. The DSS is WAY old enough to probably need a good tune-up: memory battery, key contacts, etc. and, obviously, a check for bad connections.
First, locate a shop in your area that's Korg-qualified or which at least has a tech who will talk openly with you. Feel him/her out and try to get a relationship going. Many repairs are minor and anyone who can swap batteries or disk drives can handle them. No warranty worries with a box that old, either! Korg goods are well-built, so techs know they aren't facing a maze of crapola when they open the case.
www.korg.com can give you a list of authorized dealers, who can in turn lead you to techs. Also inquire with
www.roguemusic.com; they're in NY and have many good leads to simple things such as sound disks and diagnostic tools.
A good tech will track down a diagnostic disk for the DSS -shouldn't be too hard to come by- or will know how to begin the process with whatever the DSS has on-board. Most synths have a "secret" series of button presses that lead to the real guts of the CPU. WE shouldn't use that as a rule, because you can send a synth into orbit that way, but a good tech SHOULD go there.
Bench charges start at about $35/hr. AND UP and they tend to earn it, so make a thorough list of what's wrong, as well as other requests, such as battery replacement, vacuuming the case out, etc. Don't make them diagnose things, TELL THEM! Those billable hours add up quickly! But also get the whole shebang addressed as long as its in the shop.
Take heart that it will still power up, the display works and the MIDI interface will still send, even if only on one channel. That means its a REPAIR, not a total loss situation. You'll also come out knowing more about what to do the next time it goes squonk. Good luck!