She's too beautiful to toss without putting forth some effort to make things work!
If you're set to try a repair then the first thing you should do is philosophically and practically regard the device as broken already. If you need a replacement, get one. There is no guarantee you'll be able to find the fault or fix it.
First, measure all buttons for function, ie "open" state when not pressed and "closed" state when pressed.
Before cleaning look for obvious signs of failure like some s

stain right next to a component. Get some isopropyl alcohol (99%) and clean everything. Now look out for any fishy looking solder points and/or tiny holes in components, you'll need a magnifying glass to be able to spot those. It may be you have to remove heatsinks (big chunks of metal) attached to components via some (usually white) silastic to access everything (you'll need some of that to reassemble if you found any faults).
If you can't find anything then (without special equipment that's too expensive) that's it - you cast the net and no fish were in it. You can reassemble and see if simply cleaning everything did the trick but don't count on it. If you do find a faulty part then the search for replacement (or resoldering) begins.