So, the shift key in general doesn't work?
It's not just one of them?
Have you had a proper check that the key isn't jammed or has anything trapped in it?
If you can't get it to work (and you really need shift) you could use the OnScreenKeyboard.
Also, have you tried using another keyboard (if you have one) to make sure it's not a problem with your keyboard?
Other than that, I don't really have much advice. I'm not a surgeon.