When did this problem start?  Have you installed the KB891711 hotfix
(released 8 March) from either the Windows Update site or using Automatic
Update?  If so this is possibly the cause of your problem.  Boot into Safe
Mode and using MSConfig (Start, Run, enter MSConfig in the box and click
OK), open the Startup tab and uncheck the entry labelled KB891711.  Apply,
OK and boot back into Normal Mode.

Does this solve the problem?  If yes then the problem is due to this patch
which is causing several people to see problems such as you are reporting
on previously stable systems.  If this is the case could you please post
details of your graphics chip and driver.  You can check this using System
Properties | Device Manager, click the + alongside "Display Adapters" and
post back details of the video card/graphics adapter you have installed
and then from the Driver | Driver Details buttons the version of the video
driver you have installed.

See also Noel Paton's post "KB891711 - problems?" and also that by Jerry
Bryant (Microsoft)  "MS05-002 on 9x and ME" in the windowsme.general
newsgroup.  If in n.America PLEASE phone Microsoft as requested by Jerry
on +1 (866) PCSAFETY. When calling, please indicate that you are having
issues with a security update 891711.  Microsoft need all the information
they can obtain on this problem and YOU can help both yourself and others
by ringing them.