What I would do is take all the keys off, then put the keyboard into the dishwasher (complete with soap). I'd probably use a rinse agent too to help keep deposits from forming. Make sure you DON'T use heated dry. It might not hurt, but I doubt I'd want to chance it. Let it dry for a couple of days. If your dishwasher has one one of those baskets that you can close up for small things, put the keys in there.
Once the keyboard is dry, it should work great.