The RROD on an xbox 360 is kind of a shoot in the air type deal. Three red rings is a general hardware failure, and may also show up as an E73 error code on some older systems. Usually to fix these I reflow the motherboard.
Strip the console clean of nothing but the motherboard, clean off all the thermal paste from the CPU and GPU chips, apply flux around ALL chips that you can see on the motherboard, pay special attention that you get the flux in under the chips, paying again...close attention that you flux the RAM chips as well. These will be identified as 4 smaller chips that sit 2x2 L shaped to each other.
Once the board has been fluxed, you can either put the board in a bakers rack(if you have one available that is SPECIFIED for electronics baking) or use a heat gone to heat up the flux in under the chips. Reapply the thermal paste to the CPU/GPU and you're done
What this is doing is reheating all the old solder points in under the cheaps and reconnecting them to the board if any have come loose. Usually on xbox's they run so hot that the board starts warping while they're running, heating up the solder points and popping them off the board.
If this doesn't work to fix your E73/RROD then it's usually a bricked system unfortunately.
