New company took over and outlook now having issues

You are very smart with a computer!! Everything you wrote, totally went over my head. LOL I will try the command prompt and put in what you put. I haven't rebooted the modem...too afraid it may not come up again. Ok...did the command prompt thing and it says default server- Modem.home. Then is just said Address 192.168.0.1. All of this is just Greek to me. I have no idea what DNS is. I am so lost in all of this and they outright told me it's on me to fix even though they messed it up.

No, webmail and Outlook don't have to match in their SMTP servers/ports. Either should work with Outlook, but webmail prefers the security protocol used by mail.centurylink.net port 465, i.e., SSL The SMTP server should not be involved in the problems you are experiencing.

I do see one strange thing that may be location dependent. If I try to do a reverse DNS lookup of the IPv4 address for 209.67.129.100 (mail.centurylink.net), it fails. A forward DNS lookup of mail.centurylink.net succeeds and says it is an alias for lumen.pangia.biz and its IPv4 address is 209.67.129.100. I don't know that Outlook should need to do a reverse lookup, but it is a bit strange to me. Note, this is still the case for me even though my IMAP connection is working now. However your DNS server may be different than mine. You can try it out using the "nslookup" command in a Windows cmd window or powershell.

Afterthought: Have you rebooted your Brightspeed modem since Oct 30th?

My outlook shows the first one you have listed. The webmail is showing the 2nd one and it does not allow me to change that on the webmail. As a matter of fact, they were the ones with their upgrade who changed my Outlook settings. I would assume the Webmail and Outlook should match but I am no computer person at all. They messaged me again on fb and she said she thought they had called me by now. I said no and here is more snippets for you. I don't understand authentication and how to check it. I just know that they messed it up and I need them to fix it.

I responded to you earlier, but my response appears to have been lost, so here I go again...

SMTP is your outgoing mail server. Centurylink now advertises 2 of them: smtp.centurylink.net, port 587 STARTTLS; and (on their webmail.centurylink.net help page) mail.centurylink.net port 465 SSL/TLS. I have always used the first server.

I PMd Brightspeed and they said to me that they don't handle the emails since it's a Centurylink email and they did the upgrade and I need to contact Centurylink. Centurylink admitted to me that they know the upgrade messed emails up and now claim email issues to Outlook, Android, etc, have been resolved when they have not. I called Brightspeed...on hold for 40 minutes and she said...I can't help you with email issues. I get the runaround from both. I am not a computer person at all but I looked at the smtp on the webmail for Centurylink and it does not match the IMAP...had POP before their upgrde...they don't match what they say my Outlook should say. Well, my Outlook has all the right stuff for outgoing and incoming except something called STARTTLS is clicked for outgoing. There is an SSL/TLS but when I tried that the continued synchronizing just got worse so I put it back to whatever their upgrade did which also played around with my Outlook...nothing coming in but I can send out....just takes time for things to go out and then the synchronizing over and over. It's infuriating.