Pull the keyboard apart and try cleaning it.
It's not difficult, but can be tedious and you'd want some kind of reference as to where the keys go when you're fitting it all back together.
Considering C and X are neighboring keys, I have a strong belief it'll work, but it's also entirely possible that one of the pathways on the "mat" inside is FUBAR.
If you got more time than money, try cleaning it. Otherwise, you could do like Cap suggested and buy a new one. Those are really the only two ways I see around the situtation