Try doing it this way:

Copy TB files from the old PC

- launch TB on the old PC

- go to TB menu > Help > Troubleshooting Information

- click the Application Basics > Profile Folder 'Open Folder' button

- the profile folder will open

- navigate three levels up to the AppData\Roaming folder

- close TB

- copy the AppData\Roaming\Thunderbird folder to a flash drive

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Paste the copied TB files to the new PC

- open the AppData\Roaming folder like you did above

- delete the Thunderbird folder, or copy it somewhere if you want to save it

- replace it with the Thunderbird folder from the flash drive

- launch TB

Thank you. This was the procedure I tried originally. I followed your instructions and am still seeing only the currently available emails (from earthlink.net online) and none of the locally stored emails. No address book, and no calendar. I checked the size of the Thunderbird folder on the external drive and it is 10.5 GB. Is the size the problem?

I downloaded Thunderbird to my new machine,

From where did you download Thunderbird? From this page https://www.thunderbird.net/en-US/ or from https://apps.microsoft.com ?

followed instructions to copy the Profile Folder from the old machine and pasted to the new machine.

You don't specify which instructions you followed. If you followed those given in this SUMO help article https://support.mozilla.org/en-US/kb/moving-thunderbird-data-to-a-new-computer they are precise and easy to follow. Nevertheless users often commit errors during the transfer of the entire Thunderbird folder, e.g transferring only the profile folder itself.

In retrospect it is always difficult for a helper to find the error without knowing which moves exactly have been made during the migration. I also think that you had already launched Thunderbird on the new machine, thus creating a profile and may even have created an IMAP account for your earthlink.net address (or you created it after the failure of the profile transfer from the old machine?)

So all we can do now is having a look at the actual situation in the Thunderbird profile on the new machine: Please show screen shots of the contents of the folder Profiles in ...\ AppData\Roaming\Thunderbird\Profiles\ on the new PC. You'll also see a file profiles.ini in Thunderbird: open this file in a text editor and show its contents.

Hello again. Thank you for sticking with me. I guess I was one of those folks who messed up in the transfer steps (those you had provided in your first reply). I went back through the process very carefully and ended up with all the profile information copied from the old machine to the new one, intact and available. The problem is solved.