Hey Pancake,
I have the same desk as you and had exackly the same problems after i bought it. To clean it out, i pulled out all the channels etc and cleaned everything instead, with a brush and vacuum. On top of that i cleaned out all the inputs, outputs etc with a small brush. I would really recommend doing that. However, be careful with the inserts. After i cleaned them out, the mixer thought some channels had leads in them, so the channels cut out. If this happens, just jiggle the brush around until the channel cuts back in.

I hope this helps, im not a pro mixer serviceman, but it helped stop the noises of my desk.

You should also have (2) cleaning products onhand at the same time you are using the vaccuum and the brush. Be careful around the PCBs and their IC's, as the vaccuum and the brush may induce static charges that can cook the chips.
Those 2 cleaners are a can of Caig DeOxit (spray contact cleaner) and a can of compressed air. The DeOxit works wonders on the connectors and switches (as well as the pesky faders), and the compressed air gets the dust out of the components beforehand.
Some more caveats: too much of that compressed air at a given moment will lower the operating temperature on the board/component being sprayed. Try to be conservative with its' use.
You can get anti-static brushes, as well as the cleaners I mentioned, from Parts Express. Google them and their site comes right up. Good luck!