Here is a pretty good WinME troubleshooter, courtesy of MS.
http://support.microsoft.com/support/kb/articles/Q242/0/37.ASP
To use it, I would first boot up in safe mode. To do this, press and hold the control key as soon as the computer starts to boot. You should get a Boot Menu. Choose safe mode from the options.
Once safe mode has loaded, go to start and run: msconfig (as indicated in the troubleshooter -- you might want to print it out).
Clear the check for "load startup group" and restart to normal mode and shut down to test. If you don't have the problem repeat, then the issue is with one of the files loading under the startup tab. You can selectively disable or enable those to test.
If you still get the error, try this: click the "Advanced" tab on msconfig and put a check in the box to load a standard 640x video driver. You problem could well be related to that or to your Monitor. If the problem doesn't occur with just a standard VGA driver, then you will need to remove and reinstall your Video Driver.