That is possible. But I am trying to find the cheapest way to test things out. There are things called Afunta Mini HDMI Male to HDMI Female Converter Adapter Cable Cord 1080P... Just like there are Mini-DP to DP cables and adapters. That one shows as being $6.50 on Amazon.
http://www.amazon.com/Afunta-Female-Converter-Adapter-Cable/dp/B00IZYIZKA/ref=sr_1_2?s=pc&ie=UTF8&qid=1437176567&sr=1-2&keywords=mini+hdmi
Generic Gold Plated HDMI to HDMI Mini Adapter $4.33 on Amazon. Now I see on that same page that there are other vendors selling them for $1.45 with free shipping. Not sure how they make any money doing that, but whatever... LOL...
http://www.amazon.com/Generic-Gold-Plated-HDMI-Adapter/dp/B0041TF4QQ/ref=sr_1_1?s=pc&ie=UTF8&qid=1437176567&sr=1-1&keywords=mini+hdmi
Anyways there are lots of Mini-HDMI plug things there... here is the page I managed to pull up showing those:
http://www.amazon.com/s/ref=nb_sb_ss_c_0_9?url=search-alias%3Dcomputers&field-keywords=mini+hdmi&sprefix=mini+hdmi%2Caps%2C251
We need to eliminate items as being the cause of the problem. As we do that, it will lead us to what is the problem. Since the monitor and video card are the primary sources of your display image, we need to do our best to test them first.
Earlier today, I helped someone else solve a problem with their system. It was rebooting without warning, normally in the first 30 seconds after it reached the desktop. Sometimes before it got there as well. But in the course of trying things, he discovered that this was only happening every other boot. One boot was normal and stable, and the next boot would power down within 30 seconds of the boot. Before he came here, he had already swapped out the power supply. And the problem continued. We spent most of a week trying to isolate what it was. I had reached the point where I thought his computer had to be possessed by the devil himself.
And then this morning, after I gave up and asked him to RMA the motherboard, CPU and memory, and to start all over with new hardware, he remembered that he had installed an app on his system that he knew was incompatible with his CPU, but which he figured would be ok just for checking the temperature of that same CPU. He spotted an entry in the Task Manager Startup list, and that reminded him it was there. He disabled it, and rebooted 10 times in a row to check stability, and it never once restarted on him... Problem solved.
So yes, it can be software. But again, your video card and monitor are the primary sources of what is shown to you on the display. So that is where I would like to start if we can.