Copy the full mail directory (the mail directory is the parent of your account directories) to your new system.

Now install TB.
Run TB.
As this is the first run, TB will ask whether you want to restore a backup or a new account.
Choose new account.
TB will ask for the mail directory.
Select the new location of your mail directory.
TB will ask for an account name.
Enter one the accountnames you were using in your old setup (the accountname is the same as the name of the directory it's located)
TB will see that the account files are present and will use those account settings and message base, etc.

Create as much new accounts as you had old accounts, with the same names and you're done.

This will restore most settings, only those stored in the registry are lost, but they're global settings, not important things like account properties, filters and templates.