Sorry not really an answer for you, just a thought.
Could be somthing to do with your new graphics card in the new machine ? Have you tried swapping them between the old and new machine to see if that works. IF so then thats the problem. If not then its a monitor issue, are there any hidden features on the new monitor to turn it into AV mode that you havent found ?
Not quite the same problem as yours I know, but when I linked up a new digital box the other day to a TV we received an awful picture and it wasnt until I played around with the settings to enable " RGB " that the picture became stable.
So if you are using a SCART lead anywhere in the connection try searching for an RGB function on the monitor.??