Thanks Linney, you got me thinking in a new direction. I started checking the links and have tried some of the changes. None so far have worked.
But I did try something interesting. I recreated the problem and noticed that the pointer turns into an hourglass while the screen is flickering and then back to a pointer when it stops (it happens very fast, just like the flicker does). So seeing the hour glass got me thinking about what process is running when it starts flickering. I checked in task manager and noticed that the explorer.exe process (not iexplore.exe) runs between 25-30 percent CPU utilization when the screen is flickering. After it stops flickering, the the CPU drops back down to either 0 or 2 percent.
I still don't know what to look at, but it just something else I noticed.