I am unable to boot my mac in El Capitan and Single User mode I am unable to boot El Capitan.

When I turn on the computer it seems to load fine for a while, but then this screen shows up:



When I try to boot into Single User mode, it stops loading at this point:



Then minutes later, this happens:



I've tried to repair the HD using Internet Recovery, the log says the partition seems fine:



I have also reset the PRAM several times.

The error I get when trying to boot into Single User mode seems pretty crazy. Is it likely that I'm gonna have to reinstall the OS?
Yes. Single user mode is the most basic thing your OS can do. If that fails, you either have a major hardware problem or the OS needs to be reinstalled. 

Most people make a backup and then attempt a reinstall. If you can't reinstall the OS, that pins the problem on the hardware pretty squarely. If it works, you can safely assume the software just needed to be reinstalled.