Why is my 24-inch LED display flashing black (and sometimes scrambles) every few seconds?

I have recently upgraded to a new iMac: 3.4 GHz Intel Core i7. 4 GB 1333 MHz DDr3. AMD Radeon HD 6970M. 1024 MB. Mac OS X Lion 10.7.4. I have it attached to a 24-inch Cinema Display.

Before I switched to my new iMac, it would blink black a couple of times a day. This was going on for a LONG time, but was not a big deal. However, now that I have switched to the new iMac, it is every few seconds. And it has now added the "scrambled" screen to it's repertoire. Fun. And, as I am typing this...it just went black and has not come back on.

I've read a few threads on this happening, but haven't found any substantial evidence as to what is causing this. It's beyond annoying. Has anyone learned anything new?