So I have upgraded my Ubuntu 14.04 to 16.04 version. Everything went OK, but after rebooting I've got this screen loading at least 25 minutes.
After pressing ESC I can see all these errors!
Has anyone had such a problem? What can I do to fix it?
For your current issue, I would recommend booting into a live usb installation, mounting your old partitions, copying all your data off that you want to save, and reinstall since something majorly borked during upgrade.
Look up using LVM to partition your drives, and make a dedicated data/home LVM logical volume and switch to doing full installs if you can. This will lead to less headache in the future, less data loss, and greater portability and flexibility.
If you would like to take a crack at troubleshooting this. I would boot into a live install, mount your old installation, chroot into it, and start using the journalctl command and systemctl status to see just what those services are failing on. It could be something common and simple, it may not!