is a Kinesis PCB mount or plate mount? If PCB mount you could try removing all the stems and springs, cleaning and lubing the stems, and reassembling. Not sure what would be most appropriate for cleaning the PCB, although I imagine that there ought to be some kind of aerosol spray intended for same. I'd be tempted to try something like Deoxit, but that is expensive and I don't know if it's perfectly safe for getting on the PCB. (should be fine for the switches.)
Now if it's a plate mount, by the time you factor in the labor of desoldering/resoldering and the fact that the above method may or may not actually bring it back to life, you might just want to bite the bullet and buy 104 (or whatever) new switches, expensive though that may be. Or a cheap new board with browns that you can shoot in the head, which is likely cheaper although more labor intensive.
NB: I'm a complete hypocrite as I'm working myself up to putting clear stems in my Filco, but I have tested them in a G80 board and discarded the ones that seemed off. That, and it seems really silly to spend $200 on parts to mod a $160 keyboard. (since it's damn near impossible to buy a new G80-3000 here, I'd have to order individual switches.)