many SE phones have those problems - but sometimes different causes.

1. fluid damages
2. problems with the memory card (sounds stupid - but in fact, they are sometimes the troublemaker)
3. defective keyboards
4. bad connection to the logic board

the first step would be to remove the memory card - if it works after that - be happy - you didn't have to open the phone - if not - the fun will begin ;-)

get the proper tools and open the phone, check it for fluid damages, if everything is ok, check the keypad connector - reseat it (unplug/plug it in) and reassemble the phone - if it works, great - you just saved yourself 9.99$, if not - go to ebay and order a new keypad for 9.99$ (i think you know what to do with it when it arrives ;-) )