If your Monitor is an Apple-branded MultiSync monitor , either 14-15 -or 17-inch size, made about 1996-97 , this was a manufacturing defect. A wire came unsoldered inside the monitor case which disabled the Red electron beam gun....the Green and Blue guns continue to work. Sometimes this was intermittent, but usually became a total failure .
Apple will replace your monitor for free, if you are the original owner, but you have to take it to an authorized repair outlet ( or at least I did...who knows these days ?)
BTW---the monitor I recieved for replacement had its own screwy defect...the image is slightly "tilted"..it's a quarter inch lower on the right side than the left. This was due to a screw coming loose inside that supported the cathode ray tube on one side.