Gamla adressboken

If you transfer the profile from old to new, the addressbook is included. If you are stating that you set up a new profile and did not transfer the old one, then I suggest this: '

1. copy the abook.sqlite and history.sqlite files from the old profile
2. to fully replace the default,
   • click help>troubleshootinginformation
   • scroll to 'profile folder' and click 'open folder'
   • exit thunderbird
   • paste the exported two files to overlay/replace the defaults

If you have already added entries to the new addressbook and just want to merge the old with the new, then do this:

1. click to the addressbook pane
2. near bottom of pane is an import option. Click that and proceed with the sqlite option and then select the exported files.

The problem is that I don't have my old computer anymore, I have installed a new Thunderbird, on my new computer, I thought maybe there was a backup at Mozilla... or some other trick to find my old address book.

No, backups are the user responsibility. Sorry.