Thanks for providing all the details and screenshot. Sorry for the delay.
Anyway, you probably have seen it, but if necessary, contact your local ASUS support to troubleshoot and send it back for repair if you can't find a better solution:
http://support.asus.com/Hotlines.aspx?SLanguage=enA few more ideas to try are below.
1. You really want to get to the 'advanced startup' menu at boot-up to either try getting into Windows Safe Mode, go back to an earlier System Restore point (if available), or 'refresh' or 'reset' your PC if you aren't worried about erasing everything.
Sounds like you are not seeing it, but Windows may sometimes automatically boot up to the advanced startup menu after a few failed boot-ups.
2. If the system is giving you a chance to restart instead of shutdown when the error appears, try holding the 'shift' key as it restarts to check if the advanced startup menu appears.
It may not work in this situation, but normally you can get into advanced startup by holding the shift key when you restart Win8/8.1.
3. Not sure how much this will help, but alternatively, if you want to see the boot menu, try tapping the Escape key as the system restarts or as soon as you power-up, but it can be tough to catch if you don't tap it just right.
If you can see the boot menu, try creating a Win8 'repair disk' on a USB drive with another system if available to hopefully access those other troubleshooting options.
Good luck!