The reason it doesn't show on the other machine is probably because it's set for "Windows Logon" in the "Primary Network Logon" of Control Panel.
Here's how you get it to stop prompting you for a password, after you've deleted your *.pwl file:
When Windows restarts (after a reboot) it will prompt you for a username and password. Pick a username but leave the password blank and click OK.
Now, go to Control Panel, and click on the Network icon.
From the Configuration tab, click the down arrow under "Primary Network Logon," and select "Windows Logon".
If you have Client for Microsoft Networks installed, it's probably set for that as Primary Network Logon, which means you'd always be prompted for the password. Change the Primary Network Logon to Windows Logon and you'll be set at bootup without a prompt.
By the way, for those who, like me, don't like having additional network clients installed when they're only there to save passwords, there is an alternative: DUNCE. Dunce is a freeware app that's been around for a few years who's job is to auto-type your password when prompted by Dialup networking. It can also launch up to 4 additional programs after you log on to your ISP, which can come in handy.
Dunce Download and Info