Dual boot windows 8 - ubuntu ; upgrading to windows 10

I decided to upgrade my windows 8 to windows 10. During the installation process, the computer rebooted and I got into the grub console, without having my usual menu.

I was able to proceed to the installation and use windows by choosing which hdd to boot on on my bios, but after the installation I can't boot into ubuntu again. Same issue with a grub shell.

On the grub shell, I tried to use ls (hdx,y)/ to display the information about the filesystems. Only one or two were readable, while the other always responded as unknown filesystem.

I booted on a boot-repair live disc, and was able to use the boot-repair tool, but it didn't fix anything and I still have the same issue.

Here is the boot info : http://paste.ubuntu.com/11969079/

What should I do to repair my grub install and be able to boot on linux?

EDIT: using fsck I got the following result :

lubuntu@lubuntu:~$ sudo e2fsck -C0 -p -f -v /dev/sdb6
e2fsck: Bad magic number in super-block while trying to open /dev/sdb6
/dev/sdb6: 
The superblock could not be read or does not describe a valid ext2/ext3/ext4
filesystem.  If the device is valid and it really contains an ext2/ext3/ext4
filesystem (and not swap or ufs or something else), then the superblock
is corrupt, and you might try running e2fsck with an alternate superblock:
    e2fsck -b 8193 <device>
 or
    e2fsck -b 32768 <device>

lubuntu@lubuntu:~$ 

I believe /dev/sdb6 was the partition where my system was installed while /dev/sdb2 was where I had my /boot.

I'm unable to mount /dev/sdb6 on a linux livecd.

I did it by run live-cd with Ubuntu (can be any other distro) and install boot-repair. Everything is written here: https://help.ubuntu.com/community/Boot-Repair

Run in live-cd terminal

sudo add-apt-repository ppa:yannubuntu/boot-repair
sudo apt-get update
sudo apt-get install -y boot-repair && boot-repair

Then just click Recommended Repair. This works, i have used it a few times.