Macbook Pro stuck on login screen
I've got a Macbook Pro with High Sierra that keeps getting stuck in the login screen, I enter my password and can leave it for hours with no response. I've followed various other guides on this site. First I tried to clear the vram, then I ran disk utility (will come back to that in a sec) and did first aid, says there is no problem. Tried to login again, same issue at not getting past the login screen. So I have reinstalled the OS via the Internet, tried to login again to no avail. One thing I did notice is when going in to disk utility, Macintosh HD is never mounted, but it does let me mount it straight away to perform the first aid. There are also 2 other disks to select in disk utility, 'Apple HD HTS....' and 'OS X Base System', not sure if I can do anything with these to help? Can I ensure Macintosh HD mounts when booting, as I'm guessing this is the main issue? I really need to avoid formatting as I have no backup, unless I can backup my files from disk utility at all?
MacBook Pro, macOS High Sierra (10.13.2)