Here's an out-of-the-box solution... buy a new one... a good quality wireless keyboard/mouse combo is less than $100. I know that's not nearly as fun as fixing it yourself and learning new things about DFM, but there are more challenging things to apply your curiosity to.

Bought a C64 for $395 in 1980. First used Basic for programming but got bored -- not really into playing computer games. Bought the C64 programmers guide and a book on microprocessors and learned all about machine/assembly language -- broke copy protection on a few games just for fun. In ~1987 bought an Amiga A2000... great machine at its time. Funny part is, my first degree was in Biology ('82), then went to grad school and did masters in computer sci. Enjoyed programming in '80, and still luv what I do!