Very old story. About 20 years ago these boards started failing because of two leaded power resistors (if memory serves, 1/2W) which were heating the little PCB so much that solder was melting and SMT components were falling off. Some electrolytic capacitors might have been damaged from the heat as well. Pioneer came up with an "upgraded" design, which simply lifted those two resistors about 1/4" off the board. I installed one of those and it's been working fine to this day. Alas, over the years the built-in CD drive became iffy, and the console-mounted 6-disk changer is now a dead weight. Thought of replacing the thing with something befitting the 21st century, but since the EX mostly serves as a short-range garden supplies hauler these days, it's not essential. Moreover, on the slim hope that one day my grandchildren will make a fortune selling this Limited - equipped with every possible option that money could buy in 1998 as a collector's item, everything inside should be kept original, shouldn't it?
I see. Looking at cbranning2012's pic from page 1 of this topic, looks like a pair of 2W, 2.2ohm resistors, then Dorman modified the design to use 3W instead of 2W for those two and a 3rd resistor near it which may be a different ohm value.
That alone would be very easy to repair, but the question of whether other parts are falling off is a concern especially if they are lost so they can't be identified.
The first thing to do would be pull the board and examine it, whether all parts are there. Replacement resistors are about $1-2+ S/H at a supply house like digikey, then mount them a bit further off the PCB, using the highest wattage that fits on the measured, hole spacing on the PCB. A few possiblities are below.
Through Hole Resistors are in stock at DigiKey. Order Now! Resistors ship same day
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To keep them more stable mounted higher off the PCB for less heat conduction, it might help to add a ceramic spacer to each resistor leg, something like the following, or just flood the area with thermally conductive epoxy when the repair is complete but this latter option would make subsequent repairs more difficult, and yet, would probably prevent the resistors from ever needing replaced again.
Order today, ships today. CER-1 – Component Spacer General Purpose - Axial, Radial Tubular Natural from Essentra Components. Pricing and Availability on millions of electronic components from Digi-Key Electronics.
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Edit: oops, that particular spacer is out of stock but they have others of similar enough, suitable dimensions.
Capacitors, if needed it should be pretty easy to find some of similar enough size, 105C temp rated and low ESR on digikey.
I'd just do the repair like this if mine ever fails, I have no issues using the radio for FM then I have a lighter outlet powered digital player/FM-transmitter to play files off an internal mSD card or over bluetooth from a phone.