WordPress 3.5

Since the hosting company won’t provide cPanel or PHP login details, ask them if they can generate a full backup of the website for you.

Jip, it seems that it is going that direction.

Once you have received the backup, try to get it to work. Above all, do a manual update of the core files as described here: https://www.ads-software.com/documentation/article/updating-wordpress/#manual-update

Also note that many of the plugins and the theme will probably not work with current PHP versions. However, you may be able to save the contents of the project along the way.