When it looks like your / partition can’t be mounted, it could be due to a corruption or a failing hard drive.

Boot from a UNIX live CD or live USB and see if you can even mount the main root partition on your hard drive. If you can unmount it. (More below.)

Now install GSmartControl on the live CD/live USB. Start up GSmartControl after install and look at the S.M.A.R.T. attributes of your hard drive. Anything highlighted in pink? If so - what?

If nothing highlighted in pink for your HD, that’s good. The drive probably isn’t failing.

Next, you can run e2fsck on the / partition of your hard drive. Maybe there’s some corruption you can clean up. You want the partition NOT mounted before running this. Drop into a terminal. Use sudo fdisk -l to find out which partition it is if you aren’t sure. Then (let’s assume it’s /dev/sda1) type:

sudo e2fsck /dev/sda1

and see if it’s not clean - and maybe it will fix some stuff. If there is serious corruption, you may be asked to fix a lot of stuff. There’s an option in e2fsck to say “yes to everything” - but if you get that many problems, you probably won’t be booting this thing again, anyway.