Most of the old messages are not showing up on new computer

Try this:

BACKUP

1. ensure thunderbird is not running
2. enter %appdata% in search window on task bar and press Enter key
3. this should open windows file explorer in Appdata\roaming folder
4. highlight the Thunderbird folder and copy to external media

RESTORE

1. ensure thunderbird is installed, run once, and NOT running
2. enter %appdata% in search window on task bar and press Enter key
3. delete the thunderbird folder
4. you should be in Appdata\roaming folder , copy&paste the exported Thunderbird folder there.
5. start thunderbird and all should be there

I had done all of that several times except I had not deleted the existing files in the active thunderbird profile. I just tried that but the result is the same. For example, my primary email account has messaged dating back to 220 on the old computer but the only messages showing up on the new computer are the messages that are still on the sever going back to September. In addition, there are a couple of accounts that are no longer active that have messages that I occasionally need information from. There are several emails that are older than that that I need information from. All those messages are still present on the old computer.

Your wording is confusing me a bit.Is this a POP or IMAP account. I suggest you do a screenshot of the profile folder on old computer and a screenshot of what you copied. We can work from there. if the messages were in the old profile,they should stil be there when copied. This is not a thunderbird issue, but a simple file copy issue.