Switch from Brighthouse to Century Link for internet – Outlook problem

I can receive but not send emails in Outlook.  Error message says that it requires authentification.  When we switched from Brighthouse to Century Link, we no longer had to use a modem on the secondary computer (one having the issue about outgoing).  Brighthouse suggested that all email/Outlook settings were saved on the modem.  And without the modem I would not be able send messages but could still receive them.  I have incoming/outgoing servers, etc. set to Brighthouse specifications and still cannot send.  I have set up a gmail account and copied everything to it, so if the answer is to reinstall Windows Live Mail, probably would not be a big deal.  Is that the answer?  And if so, how?  Brighthouse did this previously.