Not sure about the GPU, but you can clean a motherboard by stripping it down COMPLETELY--I mean take every single attachment off--CMOS battery, cables, CPU (!), RAM, everything. Then soak it in distilled water for a while. You can brush very lightly with a soft brush, like a baby toothbrush. Give it a gentle shake to dislodge water from the various slots, and let it dry for a few days to make sure all moisture is completely evaporated. If you have any doubt whatsoever that it's bone dry, don't power it.
If the splotches on the GPU are just on the surface, try rubbing alcohol and a lint-free cloth. Be gentle.