What specific monitor? Using what port on the monitor and what port on the video card? What cabling?

The monitor is a 5 or 6 year old Kogi The cable is connected to a VGA port.  I don’t know how to tell about the port on the video card.  The cable is the old type multi-pin cable – not USB.

Perhaps this is a problem caused by power management and not a bad video card that should be replaced.  Check your power management schemes to be certain that this is not the cause.  Turn off all power saving settings to see what happens.  The power management is found in Control Panel.

I forgot to add that you might try a new cable.

I've turned off all the power settings with no affect.  I feel certain that this is a software problem because the monitor and cable work fine when hooked to a laptop.  I just got the Dell XPS about a week and a half ago and it worked fine initially.  Then I transferred my files and settings from my laptop using Easy Transfer and since then I've had the problem.

It sounds like some setting from the laptop when transfered to the XPS is the root cause. But I have no idea how to trace it? Is the XPS a laptop or desktop?

The XPS is a desktop (model 8300). 

There may have been a problem in transferring files from the old laptop (HP Pavilion) but I don't think so.  I tried to do a System Restore to a point earlier than the transfer and it ended up with my screen being totally green -- no icons, no start bar -- nothing.  So I called Dell and they talked me through reformatting my hard drive.  Once I was back to the original factory settings and before I did the easy transfer, I was still getting the same monitor problems as before.  After a few hours of operation, the monitor goes blank and then cuts out a second or two after lighting up.  Tthen I have to shut the computer down before the monitor works properly again. 

So I'm not convinced that the easy transfer has anything to do with the problem.