how do I stop my old (archive, disconnected) email account from asking for my password?

You need to copy the messages to Local Folders so that you can then delete the unused account.

1. - click help>troubleshootinginformation
2. - scroll down to 'profile folder' and click 'open folder'
3. - exit thunderbird
4. - assuming POP, click the Mail folder and then the account folder
5. - copy the desired message files, such as inbox, sent, etc - but NOT the msf entries
6. - paste into the Mail\Local Folders folder
7. - restart thunderbird
8. - if all messages are there, you can now remove the old account.

Thank you for the detailed reply David. I was hoping to keep it in the account it is in, as the high level name makes it very clear what it contains (note that it is a VERY old email account and even goes back to a time my wife didn't want her own email account so she used mine on occasion, so she has emails in there she may want to reference). Is there a way I can just stop it from asking for the connection password, given that I (and she) would never be connecting but only perusing?

No. As long as Thunderbird see it as an account, it will attempt a connection. The solution is to move the messages you want to keep out of the account so you can then remove it.

I believe I found away around this. Select the account of interest/concern, click on Account Settings, then Server Settings. There is a section on the right, also called Server Settings. Make sure the following checkboxes are unchecked:

Check for new messages at startup Check for new messages every {#} minutes Automatically download new messages

After making these changes, I shut down Thunderbird and brought it back up. No prompt for the password. I have been in TB for a while and no dialog box has popped up asking for the password. Hopefully this continues over the coming hours, days, etc.