Just an update. I received my replacement Belkin IR keyboard the other day (the replacement for the defective replacement for the defective Belkin IR keyboard I purchased!).
Thankfully all the keys on this third unit are working. Lucky #3 I guess.
Belkin also didn't require me to mail back the second defective unit so I'm now tempted to open it up to see what's causing this problem of non-operable keys.