I suggest you start over. Be sure that thunderbird is not running. copy from c:\users\<yourid>\appdata\roaming\thunderbird to USB drive. When copying this way, Windows copies every file. then paste the thunderbird folder into c:\users\<yourid>\appdata\roaming to overwrite the existing thunderbird folder. This assumes you have already installed thunderbird on new computer.

How might I handle all the email that has come in since I started Thunderbird? I think it is all on the server. Should the POP setting retrieve it again?

Yes, big problem. if old computer is available, - locate profile and then the Mail folder and within that the account folder - extract the mail folders you need, such as sent and inbox (ignore the msf entries) - in thunderbird, install the importexporttools addon - highlight local folders, rightclick and select the importexport menu option and select one of the options to import mbox files and then select the files you exported. - that salvages the messages. to include into the account, use the importexport rightclick option to export as emil files - next, highlight the account inbox, rightclick, select importexport menu to import eml files - repeat for any other files being imported.