New PC and WLM 2011 issue

Hi:
I just purchased a brand new PC with Win 7 from local store. I downloaded WLM from MS afterwards.

In WLM 2011, I created a first e-mail address and went all fine. Howeve my second e-mail address, it does not work, .... popping up 'password' in the middle of the screen and 'authorizing' at the bottom of the screen. I typed a right password just as I did on my first e-mail address.

On another PC with Win 7, both the first and second e-mail addresses work OK, never popping up 'password' in the middle of the screen.

Just wonder why a brand new PC/Win 7, .... Windows Live Mail 2011 refuses to accepp my second e-mail address?:confused:

Thanks for your help in advance.