If some metal in the monitor is magnetised the colours may be distorted; does degaussing help? (CRTs usually degauss when you switch them on at the mains, but if not search for a button or menu item marked with a crossed-out magnet). If you have any magnets near the monitor (e.g. speakers) they may cause a problem. Does wiggling the cable affect the colour (which would indicate dodgy connectors or a fractured wire)?

My guess is that either one of the color guns is not working correctly or that the screen mesh is out or sorts in some way. In either case, it sounds as if whatever it is simply needs some time to 'warm up' -- so there's probably not much to be done about it without replacing it...

And on that note, don't go getting the urge to poke around inside to find out. Monitors work at very high voltage and there's a coil inside which steps up voltage from the mains, a pedestrian 120v, to a knock-you-on-your-ass-and-stop-your-heart 30Kv or higher. Trained technicians have a special piece of equipment to take the charge out of the coil before opening the beast up, but they can otherwise hold that charge for months or years, even after being unplugged. The coil, in concept, is similar to whats used in a vehicle to fire the spark-plugs from a 12v lead-cell, or to give a stun-gun it's disabling spark from a wee little 9v battery.

Moved to Hardware Discussion.