Agreed water is a last resort, but I have used it in the past. Some key points if you go the water route.
- Use distilled water, it is non conductive. Well it's non conductive right up to the point you mix it with a bunch of dust and dirt that is.
- Make sure the rag is just damp, you don't want water to wring out of the rag and drip down into electronics.
- Only wipe the outside and inside surfaces of the case.
- Do not wipe off the circuit boards.
- Do not use a standard vacuum and brush as they are not safe from component killing electrostatic discharge.
- Use compressed air to blow off the circuit boards.
- Do not use the compressed air to free spin the cooling fans no matter how tempting it is. You can destroy the bearings and in a worst case the fan can disintegrate.
- Open a front window and put a box fan in the open back door while cleaning. The idea is to keep the allergens moving and out the back door.
Next you need to figure out where this all cam from so you can prevent it in the future.