If your monitor shows one of those 'Signal Lost, Check Cable' things when you unplug the cable from the PC's video port, check that object to see if it also shows loss of red. If so, have the red driver in the video circuitry fixed or replace the monitor. (You can still use that monitor as a text only display on a secondary card...)
If the little signal lost thing has full colours or you don't have one, move the connected cable about behind the PC and make sure it is firmly socketted. If the red flickers in and out then, you have either a loose or bent plug pin, a broken signal wire in the cable, or a failing video card solder joint at its connector.
Unplug the video signal plug and inspect it for bent pins. If one is bent, you can try to slowly and gently put it back to its right position. If this is impossible without breaking it, you can get 'crimp on' video connectors at Radio Shark or other electronics stores (15 pin high density VGA plug), or solder ones if you're good at that.
With the PC shut down and unplugged, remove the graphics card and closely inspect the connector pin solder joins for cracks. A bright light and a magnifier are very helpful. Reheat and resolder them if they look questionable - only if you have the proper skills. Have a shop do it if you aren't skilled with electronics, or replace the card.
If nothing brings the red signal back, try another monitor. If it also shows poor red, replace the graphics card. If it shows normally, replace the red-less monitor.