If this is happening when you are booting, then it is likely that the boot files/partition is broken.

If you can boot from a live CD/USB, then you should look into doing that, mount your partition(s) and see if you can repair anything that is broken.

If you haven't done anything like this before, it isn't the easiest thing but maybe you can find tutorials out there.

I have had to do this a few times for Arch Linux, but the process will likely be very different for another Linux distribution.

If you can't do all that, then work on getting the files you care about off the drive while being booted into the live CD/USB.