Ignoring the pad fixing answer, to replace a cork is really rather easy. You will need a champagne or wine bottle cork of the actual cork variety, superglue and a scalpel or stanley knife. cut a thin sliver of cork, check it's the right size, keep cutting new bits until the right thickness that beds the key inline with the other key the cork is padding to align (or if it's a trill key/ Eb key chunk, just make sure it isn't too large to allow the key to work); superglue it on a bob's your uncle.
Leonard, June 2012