So I wonder if win 10 is activated. Do you have a win 10 licence key?
2 options - take PC to shop that you bought it off, its undoubtedly covered by a warranty and it sounds like you only had it a few days. Ask for a new one or ask them to fix it. Running dxdiag shouldn't cause it to boot loop, as shouldn't turning PC off. Only thing it should have been doing in background is downloading updates and once again, none of those should cause this.
Or you can reinstall win 10 and hope its not a hardware problem.
on another PC, download the
Windows 10 media creation tool and use it to make a win 10 installer on USB
change boot order in BIOS so USB is first, hdd second
boot from installer
follow this guide:
http://www.tenforums.com/tutorials/1950-windows-10-clean-install.html
enter the license key you have at screen where it asks for the key. If it doesn't let you, click the option "I don't have a key" and PC will continue to install win 10. Once we get to desktop we will find out if it activated before or not. It may have on last install. Hard to say.
If it doesn't activate, you can always contact Microsoft and explain what you did and they may activate it for you.