From that description, based on much experience, 85% of the time I would call that a HDD failure in progress.
If you have your apple hardware test available, boot to that. all tests will be checked except hdd, which will be partly selected. deselect all, and then fully check the hdd test and run. Should run a surface scan. If that hangs or fails that should confirm a bad hdd.
or you can use any of several other surface scanning apps. I use one I made myself.
If you have backups, you're good. Otherwise you need to decide between immediately rescuing your /Users/ data, or just trying to clone the entire hdd. It's been my experience that in ~5% of cases, the hdd checks out, never to return, when trying to do a full disk klone in that condition. (sometimes before even reaching the /Users/ folder) So sometimes going directly after the /Users/ is wise.
