[Reece]

Are you absolutely sure the noise originates in the radio or is it external interference? Plug another radio in alongside and see if they both make noise.

If it's the RCA at fault, it would surely help to have the schematic but that might be tough on such a "new" set. Couple of things to try: with the board out and the radio playing making noise, bridge each electrolytic temporarily one by one with a similar sized one to see if there's a change. Be sure you have + and - same as on the set. Studying the board you might figure out how to signal trace it to see first if the noise originates in the power supply or starting in the audio output stages and working backwards, seeing where the noise stops. You could use a computer amplified speaker as a signal tracer. A shielded input lead to the amp/speaker would have the shield connected to the RCA's common rail, and the center lead from the amp/speaker would go through a small cap (like .01mfd) to a probe that you try on different stages in the RCA.