Backup the profile on the Win7 computer. https://support.mozilla.org/kb/profiles-where-thunderbird-stores-user-data#w_backing-up-a-profile

Restore the profile backup on the Win10 computer. https://support.mozilla.org/en-US/kb/profiles-tb#w_restoring-a-profile-backup

Was the Thunderbird on Windows 7 set up with POP or with IMAP?

The answer determines whether or not you should try to re-use the old Windows 7 profile under your new Windows 10 installation.

I thought I had removed my Profile info on the Windows 10 machine, but it persists.

I've done the back-up of my Windows 7 profile and put it on a stick.

My first step is to eradicate any trace of Thunderbird on the new Windows 10 laptop.

Is there some way to do that?  I've removed the software and removed my Profile info, but when I re-install I don't get the option to configure a new POP3 account, and Thunderbird opens with a few old messages.

In which case you haven't removed your profile.

Where did you find the files you removed?

Help|Troubleshooting Information has a button that will open your profile in your file manager.

I cannot find a way to get to Help | Troubleshooting.

I removed the files by using info provided above: https://support.mozilla.org/kb/profiles-where-thunderbird-stores-user-data#w_backing-up-a-profile and just deleted those files.

I knew I would hate Windows 10.

I typed %appdata% and Windows showed me an explorer window on which I double clicked.

That took me to This PC > Windows(C:) > Users > ME > AppData > Roaming

and there I deleted folders for Mozilla and Firefox and possibly a Mozilla maintenance folder

Does that remove the Profile data?

In the main menu in Thunderbird you have Help, with a sub-entry for Troubleshooting Information.

Alternatively via the 3-bar Application Menu, |Help|Troubleshooting Information

Hmm, "Mozilla"? Look for one named "Thunderbird".

I've solved this primarily with crist1's reply.

I backed up my Thunderbird profile on my Windows 7 laptop and copied that file (almost a gig) to a usb storage device. I renamed the file the same name as the 8-character name I found in the Windows 10 Thunderbird\Profiles folder.

I removed all Mozilla software using the Windows 10 control pane (probably OK to leave it)l, then navigated to %appdata%\Thunderbird\Profiles. I found the profile file and used that filename in the previous step.

Inserted the usb storage device and moved the profile.default file to the %appdata%\Thunderbird\Profiles folder and overwrote the existing file.

It worked. I have all my old mail, all local subfolders, and my filters!

THANKS EVERYONE FOR YOUR HELP!