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Go into the advanced options for the graphics card/display and make sure it is running the display at 60Hz. I'm guessing it could half support another mode that your old analogue was set to and the graphics card/Windows might not have autodetected the change of monitor properly and reset it.

Although LCDs can accept a bit of a range of refresh rates there is very little practical advantage to not using 60Hz (in fact people who use DVI have no choice as 60Hz is mandated) and the higher you go the less likely it is to work at all. You may be in the 70-85Hz area where your controller chip is almost working but causing some artefacts.

It might also be a lose connection in the monitor somewhere breaking signal and so messing with the backlight/actual LCs.