14.04 - After update, cannot mount hard drive nor boot

I have a huge problem.

I had Ubuntu 14.04 (64-bit), and Windows 7 installed. Dell machine. I have one hard drive with partitions sda 1-3 and 5-7. The data on them are important (but not urgent).

Recently I did an Ubuntu auto-update. Firefox crashed and it didn't want to open. I did reboot - and I could not log in (Ubuntu stuck in login loop). I didn't have an Internet access, so I tried recovery mode - I did fsck, update, upgrade even run in safe graphics. It didn't help, and it changed the resolution (to worst one) of the login screen. Windows could initialise booting, but without success.

Later, trying to run Ubuntu again from the hard drive, I got this:

mount: mounting /dev/disk/by-uuid/numbersandletters on /root failed: invalid argument
mount: mounting /dev on /root/dev failed: no such file or directory
mount: mounting /sys on /root/sys failed: no such file or directory
mount: mounting /proc on /root/proc failed: no such file or directory
Target filesystem doesn't have /sbin/init.
No init fount. Try passing init= bootarg.


BusyBox v1.21.1 (Ubuntu 1:1.21.0-1ubuntu1) built in shell (ash)
Enter 'help' for a list of build in commands

(initramfs)

I typed reboot, boot from USB (Live CD) and I tried in terminal
sudo fdisk -l. I got: sda1 (USB).
In /dev/ directory I can see only sda and sda1.

I did reboot. It went automatically from the Live CD (try without installing). Failure. Rebooted, I had a booting menu from the hard drive, I typed reboot in the console, and run from the Live CD.
In /dev/ I could see all sda1-7, and sda.
sudo fdisk -l shows sdb1 (usb) only.

Then I tried fsck all of them, with the result:

Attempt to read block from … resulted in short read while trying to open…
could this be a zero-length partition?

I tried:

sudo mke2fs -n /dev/...

Got superblocks numbers. I tried them one by one, without success:

> *mount -o sb=alternative-superblock /dev/sdaX /mnt*
Can’t read superblock

reboot, didn't boot from Live CD, hard reboot.

Succeed to boot from the hard drive: ubuntu -> advanced options -> recovery mode

EXT4-fs (sda6): INFO: recovery required on readonly filesystem
EXT4-fs (sda6): write access...

JBD2: recovery failed
EXT4-fs (sda6): error loading journal


(...)

mount: mounting /dev/disk/by-uuid/…... on /root failed: invalid argument
mount: mounting /dev on /root/dev failed: no such file or directory
mount: mounting /sys on /root/sys failed: no such file or directory
mount: mounting /proc on /root/proc failed: no such file or directory
Target filesystem doesn't have /sbin/init.
No init found. Try passing init= bootarg.


BusyBox v1.21.1 (Ubuntu 1:1.21.0-1ubuntu1) built in shell (ash)
Enter 'help' for a list of build in commands

(initramfs)

I tried it twice, the same result. After that I booted from Live CD (USB) twice - I had result as before (only Live CD visible in the result of sudo fdisk -l).

Any suggestion what could cause the problem, how can I fix it? Can I have the data back?