Sadly your logic board has failed (CPU) there is nothing you can really do to fix this other than replace the logic board. Here’s the IFIXIT guide to take it out [guide|33077] and here is one source for the replacement logic board: [https://www.thebookyard.com/parts-mac-mini-intel.php?cPath=96_400&sort=2a&filter_id=12|UK TheBookYard - 2014 Mac Mini logic boards] Find yours from the listing to then locate the Apple P/N then see if you can locate the logic board where you live.
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Depending on the model you might consider jumping to the just released Mac Mini. Unlike yours the new model has serviceable RAM so you can upgrade it to what you want at anytime. You won’t be able to reuse the SSD or HHD drives and the new model has a soldered flash drive so you’ll want to look for an external cases to house your drives.
What happens when you boot up in Target Disk Mode? Hold the '''T''' key when you restart your system. Do you see the Thunderbolt Icon on the screen?
Reference: [https://support.apple.com/en-us/HT201255|Mac startup key combinations]