Error in root flesystem (abridged output)

Solution 1:

I'm not too sure if this will work but considering that your linux file system passes the test, perhaps run a SMART test in the disks app on Ubuntu (on LIVEUSB) on the FAT boot partition on your primary hard drive. Maybe it is an issue with that if you have it? My PC has a partition like that. Also check your linux (ext something) partiton again the error could be GRUB telling you something is wrong with that.

Also, I noticed that it is mounted at /dev/sda5 (my Ubuntu computer starts at /dev/sda1, 2 etc) and that the error is with Hard Disk 2 so maybe SMART check the other drives connected if you have any and try booting with the non-essential drives disconnected.

If you have REALLY important data on the drive, I it might be dying so don't use it again and take it to a data recovery place.

I used to have a faulty HDD that sometimes came up with a BIOS error and sometimes booted normally. It was dying, but I got to use it enough to get the data off before it died. Maybe if you can quickly use it and if you want to save a bit of money just quickly get the data off.

If you do have a backup, managed to get your data off or don't care about the data on your drive, just get a new one and swap them out.