look at the physical circuit - does it have discolored, burned, misshapen, disconnected or melted components
if printed circuit, are any traces lifted or broken
any cold solder joints (dull instead of shiny)
get a schematic if possible - this will show you what is connected to what, parts values, voltages
poke around with a probe while it is turned on - see if this causes a change for better or worse when you touch different components
feel the componrents - are they too hot (know what you're doing here or you might get a rude surprise)
if worse comes to worst, pull out components like transistors and capacitors and test them
if it's an audio circuit, and you have one, use a signal tracer to follow the signal through the circuit to see where it changes for the worse or the problem occurs
replace or substitute ic's
if all else fails take it to a repair shop
i'm sure others have their favorite tricks too