It could be as many different things as there are components on the boards. I believe this is a handheld? Honestly, I'd say it has done its job well and it's time for a new one. I know that isn't what you asked.
Especially with a handheld, how certain are you that it isn't working? Is it not transmitting, not receiving, not powering on, all the above?
You could go through a standard troubleshooting sequence by verifying each stage - audio, oscillator, PA/mixer, receiver filter(s)... you'd need the schematic for it and some specialized tools. Or, you could go buy a new one.
http://support.radioshack.com/support_electronics/28525.htm