Ok then your PC and its connectivity are working perfectly and as you would expect with ‘Account A’ but won’t let you near ‘Account B’.
The issue has to be with the way that you have set up ‘Account B’. If you had an issue with your PC in general, or with Yahoo Messenger in particular then it would not let you near either account.
I don’t know enough about the inner workings of Yahoo accounts to be able to advise you further – but one solution may be to contact the Yahoo tech help service?