Here is my motherboard....it's relatively old and... simple. The two heatsinks on the left are connected to each other by a copper tube, and need to be removed, both at the same time.
All three heatsinks I've shown also have thermal tape, thermal pads, or thermal paste. Sometimes like with thermal tape, it doesn't WANT to come off.
There are also about 3-4 jumpers on this motherboard which have to be removed as they will get "washed off" the motherboard in a dishwasher.
Also present are 2-3 switches, which will not dry like open air components. Here you would need electrical contact cleaner, to properly dry them.
Trust me, unless you have to money to replace the component you are attempting to clean in the dishwasher, don't do it.
Vid cards are even worse, they have numerous heatsinks, and are mechanically much more complicated to disassemble.
Just blow the dust out with canned air or an oil-less compressor, once every 5-6 months and you will be fine.
