Inspecting the connectors is the most important item on everyone's list.

But getting inside a radio is not for the faint of heart and I just recommend "send it into a repair shop". The most I have ever done was replacing the fusable link inside a Microaire radio (reversed battery) and that was touch and go. These things are just too compact/complex unless you are REALLY good at this.

About capacitors. The most common aliment seems to be the dielectric expanding due to heat and poor manufacturing, which changes the capacitance. At least you can tell right away because the silver cap has bulged, sometimes cracked. I have repaired many (non aviation) items by just replacing caps..