
So what does a person do? You'd have to take apart your monitor just to get in there to clean it.
Well, i'll share a tip for you all, there are free tools available on the web that can do this for you, and without dismantling your monitor.
For an LCD screen like i have, you need a tool that is coarse enough to really get in there. If you have this type of screen i recommend this screen cleaner:
http://home.tiscali.dk/ulrich/screencleaner.swf
However if you have a glossy screen, you don't want to use such a coarse scrubber as the one above. It may leave scratches. So the below link is what you would want.
http://www.linein.org/media/screenclean.swf
Hope you find these useful.