Restore old drupal (v6) site into subdomain


few years ago I had a drupal 6 website which I’d like to restore now.

I think I have all the necessary backups (full db backup generated from phpmyadmin + full website backup generated with backup and migrate module), but even if the import processes seem to complete fine (I tried both in different clean installations) I never get any content to show up.

The website was originally in it is now installed in (the db name has changed form the original one).

I am really not an expert and while I’m trying to dig info from existing webpages, I simply think that I lack some key understanding of how Drupal and restoring mechanisms work.

I do not understand if there are problems with the restore process or if there are other steps that must be taken before/after restoring.

If anybody could give me a hint on how to proceed I would really appreciate it!

Thank you

As clarificiations:

I do not need to bring back up the site exactly how it was (themes, modules,…), I am trying to restore its content so that it would be visible as a legacy (unmaintained) site.

Furthermore, since all of Drupal6 is now unmaintained I would update to Drupal7 as soon as I manage to complete the restore. I’m working with this approach, because I understood that is not wise (probably is not even doable) to restore a D6 backup into a D7 installation. If this is a wrong assumption of mine, I’d be happy to know and to restore directly to D7.

Drupal version: