If it's dust, I usually just scrub the board with a dry tooth brush, and/or a paintbrush I've given a "haircut", to make the bristles shorter and stiffer. Finish by blowing the last loose dust off with compressed air. If you don't have access to a compressor, you can buy canned air. If you have, make sure it's an oil free one, or that it is equipped with a liquid separator.

For more grimy stuff, the same tools combined with some electronics cleaning agent would be my weapons of choice. First clean off whatever dirt you can with a dry brush, then give it a go with the cleaning agent. Finish by blowing it off/drying with compressed air. Be careful to let it dry up completely before powering the board, those agents usually are extremely flammable. It might take some time for fluid trapped under IC:s and other components to vaporize.

I generally use isopro to spot clean boards, but I immediately clean it off when I'm done. For general application, at most I'll use a damp cloth.

To clean hardware, I'm usualy using ... a shower and soap. If you remove the battery and dry it properly when you're finished, you shouldn't have any problems. Not only this remove most of the dust but it also remove a bit of the smell that some hardware may have after years. It doesn't remove it completely though, but at least it's clean and it smells less. Maybe if you brush the board when you're using the shower will do the trick ? (Sometimes dust is stuck so munch that even hot water can't remove it by itself. But using a brush may help)

You're right. The mainboard smells really bad. More than any other boards i've ever used and bought.

Do you really think, a shower is OK? I don't know if the water from the shower is good... Even at my home, the water has a high concentration of calcium carbonate.

You might not get rid of that with a shower. Water, soap and brush are more for baked dust and mess that has been caused by water. I would first unsolder the remainder of this abomination and then clean with 'spiritus'.

I clean boards using liquid dish soap, a soft brush and hot water. Leaking caps I clean with alcohol and a Q-tip. If your area has hard water (leaves calcium deposits) do a final rinse with distilled water.

Generally it only takes a day or two to dry the boards off and they look new.

Lately I have been using only Acetone for cleaning residue from desolder/solder work. Works well. Other than that alcohol.