OK, I have learned a little bit more.

I did not have the Dell 2000FP drivers installed, it was set to Plug
and Play Monitor. SO I Changed that, no change inthe problem.

But then, I dropped the resolution from 1920x1440, true color, 60 Hz to
1280 x 1024, true color, 60 Hz and the problem goes away. So I went
back to 1920, and noticed that the screen is panning some (ie, the
screen is bigger than the physical display, I can slide the mouse for
example to the left and the screen adjusts over that way. I also
noticed that in the Display Properties it acts like there could be 2
monitors, maybe because that's a function of the ATI card? The ATI
Catalyst Control Center says the second display is not enabled, but if
I enable it I can use it. But there is no second display?

I also noticed that the ATI Control Panel only goes up to 1600 x1200,
when I have been using the same ,monitor and my old display card at
1920 x 1440 for a year. Also, it appears the monitor supports up to
2048 x 1536 true color, 60 Hz.

I really have a hunch that the blinking (that's what it's like, a small
blink) is because of the panning, some sort of reset of the screen, or
the second monitor that's not there. But I am very confused right now.

Does this shed any light on the situation for anyone, or give anyone
some clues how they would continue the diagnosis?
Thanks so much for your help!