Here are the steps to successfully rid yourself of the Network Logon screen:
1. Go to the Network applet in Control Panel.
2. In the 'Primary Network Logon' box, choose Windows Logon. Click OK. Do not restart.
3. Go to Start --> Find/Search, and search the C: drive for *.pwl files. Delete all that appear. (These are Windows 9x/ME password list files and it is perfectly fine to delete them.
4. Reboot your machine. You will receive a logon prompt, type in your name, leave the password blank, and confirm the blank password. Once you are done, reboot to confirm that no logon screen appears.