Two keys not working

We've suddenly lost responsiveness from the Q and W keys on our iMac USB keyboard. It's one of the nice ones with a numeric keypad and a good tactile and auditory response, so I'm loathe to replace with a keyboard more recent.

So far I've tried

1. plugging the keyboard into a different computer — confirmed that the problem is with the keyboard
2. removing the two keys and cleaning underneath them — surprisingly clean to begin with, given that this was the first cleaning in all the years we've had it

Under the keys, this keyboard looks to have a nicely sealed rubber membrane. I couldn't see how to open up the back, though, as there are no screws there, and no obvious catches to release.

Any suggestions on where I should try next?

For now, I've got a Logitech keyboard plugged in but it's nowhere near as nice to use as the original Apple one.