Ah Windows ME, I am not sure what it is that you want? This password/logon is only for network connectivity - not access to the computer - if you want to restrict network connectivity to authenticated users you choose the Primary Network Logon to Client fof Msft Networks (You also have to create an user name and password if you want one.) and use a password, if do not want user authentication choose Windows Logon, and assign a blank password.
Control Panel >Network>Primary Network Logon > Windows Logon or Client for Microsoft Networks. If its no logon is what you want, on the first reboot after making the changes, it will still ask for username and pwd, so select the default and tab to the pwd and hit ok.
I am getting on in years and that ME was a particular PIA so I might be a little fuzzy on the details here.