The best way to recovery my data in an old failed ubuntu

This is something you will do only once, so you need not set up a perfect environment in the live system.

- Have you mounted the partition with your data? In that case maybe it is mounted with read permissions only for root (the superuser), not for your regular user.

Either you change the mounting so that your regular user will get permissions, or you save the file with a tool, that runs with root permissions.

- Do you need help with mounting the partition with your data?

- Do you want a graphical user interface, or can you use terminal window commands for saving the files?

cp and rsync are good command line tools

sudo cp ...
#or
sudo rsync ...

sudo add-apt-repository universe
sudo apt-get update
sudo apt-get install gksu
gksudo nautilus &