If you are going to do as suggested above make sure that none of your devices that can access your email account are online because T'bird will try to synch with the servers and if all the emails have been deleted from the server it may well delete the ones you transfer from your old PC hard drive into the folders on the new PC and new install of T'bird.
I would strongly suggest that you do a back up of the T'bird folders from the old PC before doing anything.