CompuServe Messages

I'm experiencing problems using my a1200 with my new 1942 monitor. The screen displays a background interference that almost looks like flickering. This occurs in all modes, including non-interlaced resolutions. The 'flickering' is worse during hard or floppy drive access and when the cpu is heavily engaged, (sorting a large directory in memory for instance). This problem was not noticeable when I used a 1084 monitor. I suspect the computer because mine is an early version a1200 and I vaguely remember a problem like this being mentioned when they first came out. Can anyone verify what this problem is? If it is my a1200, is there a fix available? My Amiga is out of warranty so I need to fix it myself if possible. thanks for any input, Ray