OK, just in case someone has the same problem in future. I left the mini in the hands of a tech guy who couldn't figure it out. But then, someone on Apple discussions pointed out how to solve this issue.
Basically you leave it unplugged for a night, plugged in it, press cmd + alt + p + r along with the power button of the Mac mini.
Now, this might not work right away. If it doesn't work right away, unplugged it from the wall again, leave it for 5 min, then plugged it back in and try it again.
The person who mentioned this said it took 4 days and over 200 tries before it turned back on. For me, it took 2 tries and it worked.
This is also why it happens:
The EFI firmware on the pram has been corrupted and the instruction to start the computer is not being properly executed. EFI firmware is the same as the BIOS on a windows machine
I have a similar issue: if i live my Mac mini 2011 off for a night, it will boot and start sierra, and then, after a few minutes computer will shut off by itself, and if i try to turn it on again, all i get is the cooler at full speed and no screen at all (not white not black not grey no logo, nothing). At this stage only fans work, no other noise of booting, forcing me to shut down computer by holding power button. After a few ours unplugged, it will star again, and same problem occurs, finally shutting down computer and secondary problem start (fans at full speed) . Any help would be very appreciated.
"I would like to thank everyone who shared this information. I turned on the device that the Apple service said it wouldn't even be able to do. Out of joy, I kissed the cat at home over and over again.
And yes, whether it's sleep mode or other options, it works tremendously.
Note: I made a thin cable line because the new SMD equipment is large. I got this cable from the old HDD ide cables. And camouflaated it with fireproof flex tape. When I was dismantling the old piece, I put liquid flux on it so that my solder would be easy to separate."
