You didn't really give enough information as to what is causing the "Enter Network Password" box or a good description of the box for me to make a definitive decision about how to resolve it but here are two guesses..
1. If it happens when you are in Outlook, you could have an extra mail account setup in Outlook and it's trying to access the extra mail account which is not setup properly. Delete the extra account and it will go away.
2. Internet Explorer is set to dial a connection when a network connection is not present. To correct this, open an Internet Explorer window. Go to the Tools menu, click on Internet Options. Choose the Connections Tab and make sure "Never Dial a Connection" is chosen, click Ok. Close the Internet Explorer window and reopen a new one. This should take care of it.