In the Windows ME PC, open the Network Properties (right click "My Network Places" and select Properties). Ensure that you have both of these installed:
- Client for Microsoft Networks
- File & Printer Sharing for Microsoft Networks
Click the "File & Printer Sharing" button and check that one or both boxes are ticked as appropriate.
I would suggest you set at least one Folder as "shared", rather than the root of "C" drive. Have you configured any firewall software in the ME PC to allow access to the other PC?
Also, it has been known to help if you use a Workgroup with a name of your own, instead of the Windows' default name.