The account password isn't going to work no matter when you enter it. AT&T accounts require a secure mail key for TB instead of the account password.

https://www.att.com/support/article/dsl-high-speed/KM1010523/ https://www.att.com/support/article/email-support/KM1240308/

Got a new security key from AT&T but no place to enter it in thunderbird so don't know if it will fix my problem. My problem is that inbound messages arrive fine but when I send email it goes right to "Sending Message" forever: an infinite loop. It doesn't say message failed or enter password or anything, just and infinite unending loop with message "Sending Message" which eventually ( half hour and longer) I click on CANCEL. I've spent more than an hour on my cellphone with ATT and finally got the new secure key code but that makes no difference as there's no place to enter it on either att.com or Thunderbird. As a matter of fact TB no longer shows GET MAIL or WRITE on its menu bar. I have to dig it out by clicking other things just to create an email message which goes back to that infinite loop.

Have you checked in Account settings > outgoing server (smtp) that the outgoing server is set to require authentication? I have lost count of the number of folk not being asked for password having set the authentication to none for some reason.