You'll have to experiment...noise works in mysterious ways.
1) Plug the monitor's AC line into a different circuit, or at least another outlet than the rest of your gear. If it's already on another circuit or outlet, try plugging it into the SAME circuit/outlet.
2) Try moving the speakers, monitor, or other components near the monitor farther away from it (maybe it's radiated interference?)
3) Are you using any of the cheapo interconnects that came with your gear? Try upgrading to shielded interconnects. No need to spend big bucks on exotic cables - just buy something that says "shielded" on the package and looks fairly heavy and well constructed. Top of the line Radio Shack or similar should be more than adequate. Your speaker cables are unlikely culprits so don't worry about those.
4) Is your monitor or whole system on the same circuit (or even in the same room as) "noisy" devices like light dimmers or florescent lighting? If so you may need to plug everything into a different circuit. Or buy and install quieter dimmers. Or do away with the florescent lights. (Florescent lights and dimmers are more likely to induce a "buzz" sound instead of a hum, tho...)
5) As a last resort that requires real money, buy an isolation transformer and try placing it in the signal path (i.e, your audio/video inputs/outputs) between the monitor and other components until the noise is gone. For example, see:
http://www.markertek.com/Product.asp?baseItem=JEN-CI2RR&cat=INTERFACE&subc
at=&prodClass=AUDHUM&mfg=Jensen+Transformers&search=0&off=
You DID read the grounding thread here, didn't you? If not, consider it required reading before proceeding and posting further!