Do you still have the old computer? Remove the Hard drive and install it in a USB case (Assumes the HD was not making nasty noises or failed electrically) or a 'transfer adapter' .
Simply copy the OLD Library folder over to the new Computer (
Do NOT overwrite a non-empty Library), giving the Library folder a New name (the folder name is the Library name). Then right-cick the Library Icon in Calibre: Switch/Create: USE EXISTING: <point to the new folder>