Thunderbird does not provide mail accounts or have passwords of its own, unless you are referring to primary password see https://support.mozilla.org/en-US/kb/protect-your-thunderbird-passwords-primary-password. If you do not know what primary password is, see the screen shot there.

If you are referring to a mail account, you must use the services of your mail provider to reset your password.

No, no primary password.

I have tried to reset my password many times: It never works -- when I try to log in with the new password, Google pops up, asks for my id ([edited from public] @gmail.com) and then demands a password. No new or old password allows me to log in. And, with 2-step verification on, I can't seem to get a 'phone call; just a demand for the 6-digit code suppose to have been phoned to me.

Gmail is completely broken!

re :After reinstalling thunderbird, all I can enter is the first user page: Name, Email address, and password. Nothing further allows me to use thunderbird!

Check the Firewall. Thunderbird must be an allowed program otherwise your Firewall may be blocking access.

If you have a VPN switched on then switch it off.

Have you removed the old saved passwords from Password Manager?

• Menu icon > Settings > Privacy & Security
• Scroll to Passwords section
• Click on 'Saved Passwords'
• Click on 'Show Passwords'
• Select the gmail accounts - there may be more than one line and click on 'Remove'
• click on 'close'

If you are using 2 step verification: Try Sign in with App Passwords

• https://support.google.com/accounts/answer/185833

Then you use the 'app password' instead of normal password when you get prompted to sign in.

Is there a particular reason why you are using 2 step verification? If you switch it off and in Thunderbird use Authentication Method 'Oauth' then you do not need any 'app password'.