A few keys don't work at all. Other keys work just fine.

Four of the keys on my keyboard, (the left and the right arrows, the tilde (~) key, and the right command key) are not working. There doesn't appear to be any physical damage to it, at least nothing external. All other keys work properly. An Apple Service Centre and the AppleCare people (on phone) told me that "No Authorised Service Centre will repair Keyboards or Mice". (I should also mention that the keyboard is 4 years old.)

What could be wrong with it?

Is there any way to even (non-destructively) open this thing up (and then put it back together!)?

The Model Number is A1314