Are any other email accounts working on the second computer? Could the firewall be blocking Thunderbird?

As previously stated, "I HAD two different T-bird email accounts successfully running on my THREE computers."

Currently I have my new T-Bird, @gmail account running on my three separate computers.

However, T-Bird will only let me create an @outlook.com account on one of the computers.

You "had", past tense. It doesn't quite tell us what is happening now.

So, you had two accounts, both running on each of three different computers?

Why are you "changing" account names? Are these not new accounts, offered by the new provider? I always advise setting up new rather than adjusting existing accounts in an email client.

Since you have it working on one machine, can you not copy the settings over to the non-working instance using the manual set-up option? Take Thunderbird offline if need be.

I don't like MIcrosoft's mail offerings. If I search for server settings I'll find multiple and conflicting suggestions. When I had to work with a local MS Exchange server, I could sometimes use IMAP/SMTP and at other times (at the whim of a sysadmin) I'd have to use Davmail to connect to it as if I were using the outlook email client. Currently we're using Office 365 here, so it's yet another set of settings and a totally independent password that expires when Microsoft says it should, and the only hint that the password has expired is that it fails to connect - no polite message asking me to change it. I have to ask my sysadmin for a reset several times a year because it is so inelegant in operation.

All in all, a mess, and I'm not surprised you have trouble with it. But since you do have it working on one system, you have concrete evidence of settings that do work.

Has outlook.com ever refused multiple connections? IOW, does it mind if computer#2 connects at the same time as computer#1?

1. Previously my ISP was Windstream. My two email accounts were with them. I prefer T-Bird for my emails, and created two accounts: two different usernames ending with "@windstream.net. Had both accounts working on my three computers. One is a laptop; was able to access both accounts regardless of my location. 2. Windstream DSL became dreadfully slow so changed to (DISH) satellite connection. Discontinued @windstream & signed up for Outlook. Using T-bird I created an @outlook.com account on one computer. Attempts to create @outlook.com T-bird account on either of remaining computers produced the Invalid error message. 3. Went to Gmail. Created '@gmail.com T-bird accounts on all three computers, using same username and P/W. 4. Tried to create a second @gmail account with a different username. T-bird came back with the Invalid error. Tried using same, and different P/W. No luck. I need two different accts on all three computers.