Question PC shuts down when accidentally hit from the front

Hello
First of all. I can not afford at this moment new PC either build myself or buy, please no suggestions like those.

Problem. My PC is sitting under the desk, on the floor and once in a while it get kicked (not strong, but enough to create vibration, I guess). Then it shut dons, sometimes completely, sometimes it is going into the loop of shutting down, then attempting to restart on its own, then shutting down and so forth. Everything inside is firmly secured, no loose parts, checked all cables and connections, nothing wrong. The only fix so far is to turn power off on PSU and leave it alone for at least 1 hour.
After time passed (at least 1 hour if not more) PC starts with the message that overclock failed, enter the setup - when I saw this message for the first time, I reset my mild overclock to factory default, but with every new incident I see the same message, so I just enter the setup and exit it with "Save changes". And until the next time.

What I have.
Win8.1, 4790K with Noctua ND-14, Asus Maximus VII Hero, GTX 1080, Samsung SSD, Creative Sound Card, EVGA 850 watt PSU (some Gold model) and 16 GB RAM (don't remember which one, but one of the recommended, for sure) and 6 HDDs for storage (all NAS and Enterprise quality).

This PC just celebrated 10th birthday last month and it will be changed, but, unfortunately, not now.

Any ideas what is happening when kicked from the front (I can move PC back and forth when it is working, no problem, sometimes it got vibrations during those moves - nothing happens)..

Any ideas/suggestions appreciated.
 
The only time I've experienced this personally has been bad wiring (be it power or data). When you checked all of the connections did you unplug them and then re-plug everything in?

Not that it's a great idea to try to get it to go off on purpose, but one thing I'd suggest trying if you want to go that route would be disconnect all of the HDDs (should be able to just unplug power) and see if it still happens.