One thing you may want to try before tossing the monitor (if previous suggestions are of no avail) is to take the back cover off and use a can of compressed air to blow all the dust off the components. I've seen monitors do some pretty weird things when they get dusty.
Just be careful not to touch anything. There are a few capacitors in there that can kill you if they're still charged. To be safer, if you turn it off and wait a day or so, they should all be drained.