I found an interesting article about how to clean your computer.
It's located here:
http://computer_collector.tripod.com/vintagecomputers/restorationindex.html
I also mailed this collector about how to remove the yellowing from once white computers. I post it here also. Good luck!
Hi, I just stumbled upon your page, you have some nice tips for cleaning old computers. I managed to reduce the yellowing on some of my computers and monitors by using the following product: Muscle Super Degraissant. Is made by Johnson wax (update: Glassex also has a Super Degraissant nowadays).
Don't know if you can buy that in your country. But I think Johnson is a very common brand. Ok, When I moved to a new house 3 years back, the whole family was helping out with unpacking. My brother saw the boxes of my soundsystem: they were yellowed. You know these boxes, white, plastic or white plastic layer on cheap wood. He had nothing to do, so he went to the kitchen to find something he could clean the boxes with. They only thing I had in the kitchen was Muscle. Being my brother, he took it and sprayed it on the plastic of the boxes.
A miracle happened, after cleansing the boxes where white AS NEW. Being a computer collector later on, I remembered this. Please note it's aggresive. I always try it first on a small spot on the back or the bottom of the monitor or computer in question. Depending on the plastic used, how much yellowing and how old the comp/monitor is, the results may vary.
Be extremely careful with "sprayed on" plastic coatings and bumpy surfaces that are not totally flat. ( "poreus"

. Make sure that you always handle one side of the computer/monitor at the same time. e.g. do not spray on the middle of the side of your monitor and then walk away or something. You know what i mean. Else you would get bright spots on your cases and we don't want that. If there's only a little bit of yellowing, you can also spray the stuff on a little piece of old cloathing, a towel etc. and then rubb the surface with it. (again, one side of the case at the same time. else you get differences in coloring). Please note that when you do this when there comes to much nicotine and tar out of the surface you might ending up smutching the yellow stuff over the rest of the surface (like the smutching tool in a paint program)
Always rinse with clean water afterwards to remove possible residues of muscle. Else you might get suprises if this stuff continues to works on the surface. Make sure you clean the cloth were you remove the muscle with after each surface. Else you end up smutching the dirt like stated above. Some results:
5 year old monitor -> yellowing -> muscle -> 97% gone. (hard plastic surface but bumpy)
13 years old Sony MSX2 HB-700P: front panel -> sprayed on plastic on plastic surface-> heavy yellowing -muscle - 70% gone (this was a "quick" one, waiting to long here with rinsing would eventually lead to the dissolving of the plastic.
13 years old Sony MSX2 HB-700P: top case white, yellowed paint on metal -> muscle - 100% gone (e.g. 100% white again)
13 years old Sony MSX2 HB-201P: one case, yellowed about 20%) ->muscle -> yellowing complete gone.
10 year old monitor, extremely yellowed, heavy spraying (the thing was broke anyway), about 60% more white.
But Muscle is -until- now the best thing yet. I also found out like you mentioned that VIM (I think that the stuff is called CIF here, to clean your kitchendesk etc. right?) indeed solves all those blacks marks.
Viewing the process:
I'll describe viewing the process. When you use the spray directly on the surface, the surface will "sweat out" (you see this!) nicotine and tar and other dirt. The active elements in muscle somehow react with that dirt. Leaving the plastic itself alone most of the time, depending on the type of plastic and how long you let the muscle react with the surface. Never let muscle react longer than 10-20 seconds with the surface until your build up your own experiences with this stuff.
Please note, I use Muscle now for over three years. some surfaces, like the monitor i use for my pc, have had more than one treatment. The logo printed on the surface also had his share of muscle (try to avoid that) but the paint hasn't come off. The plastic is white and stays white. There is no viewable side affect after using this three years on the same monitor. (so no decoulering etc.) The plastic didn't become poreus (bumby) after using muscle.
Well, just try it out for yourself.