well on your chassis you have or should have the following adjustment pots verticle hold,verticle position,horizontal hold,horizontal position,contrast,brightness,horizontal width,verticle width,these could be situated on a remote board-just because you cant see it dont mean its not there.when i refer to caps i mean electrolitic capacitors,over time these componants dry out and can give faults like the one you describe,if you have a little experience with a soldering iron you can replace all your electrolitic capacitors with very little expense,only a little time.please can you tell me what chassis you have or take a photo of it so i can try and reduce the time it takes to locate your adjustment pots.
as for your other monitor it sounds like one for the skip,but if you know the chassis type you may be able to purchase a new/reconditioned chassis at little cost.again if you post a photo i may be able to identify your chassis type.