I see, I am no expert but it seems to me that since it is happening with your xbox and laptop (most importantly xbox) as well, your graphics card is probably not the problem.
It could be there is something wrong with the Monitor itself, in that case your best chance is to probably buy new cables and try that or eventually a new monitor. You could try using the monitor with a third device.
I got a super nintendo from 1987 that had not been used for ages, it didn't work, I opened it and cleaned all the dust in it, to my surprise that fixed it, and now works like new. Maybe if you did something to your monitor along those lines, you have nothing to loose really, since the warranty is voided.