This sounds like a hardware issue. Microsoft has had so many problems with shutdowns in ME and 98 that they have developed a special application to help resolve hardware issues at http://support.microsoft.com/support/kb/articles/Q239/8/87.ASP.
If this does not help, the best I can tell you is to search the TechNet site (www.microsoft.com/technet) for Windows ME Shutdown keywords. You will find quite a few Knowledge Base articles on the subject.
Dig deeper on Microsoft Windows Data Backup and Protection
Have a question for an expert?
Please add a title for your question
Get answers from a TechTarget expert on whatever's puzzling you.