-thanks to HowSuffWorks for the image below.
Step 1: A word of warning...
As mentioned in forum (above link)
The unit would have to be disassembled to clean it out. That is a job for a professional.
Have you checked with a PC repair shop to see if they can do that (and guarantee their work in case they mess it up).
-I've already taken laptop screens apart, so I had a rough idea of what to do. ;-)
-If you want to attempt this, having taken apart electronics &c. is recommended. Please Note: you may be able to get a replacement if your monitor/laptop is under warranty.