Sounds like a bdy [edit: bad] keypad.
If you use a jumper wire and connect the two pins that make up any keypress, can you see all the characters?
For example, put a jumper wire on 6, and touch it to 2,5,4,3, then 7 and 2,5,4,3, then 8 and 2,5,4,3, then 9 and 2,5,4,3.