Now there is no sense in having two computers.
Why, because of the password issue? That makes no sense. You either have a need to get your email on two computers or you don't.
I have Windows Live Mail on another computer and I could never get it to handle more than 1 email address.
Don't what your problem is there. Windows Live Mail, and every other email client that I know of, can handle multiple email accounts. I have 5 email accounts in Windows Live Mail.
I have always used Outlook 2000 and it has always worked just fine. Now I have two computers that keep asking for a password.
Do you know how to save a password in Outlook? Please explain exactly how you believe the procedure works. Have you changed your password recently? If you access your email account via web browser, does the same password work?