Are you able to boot it up in safe mode or under the onboard diagnostics? [https://support.apple.com/en-us/HT201255|Mac startup key combinations]. I would start there. If you can't, are you able to get it to get the system into Target Disk Mode? Let us know what works and what didn't that will give us a clue on whats needed here.
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=== Update (04/03/2018) ===
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Well then, I think you'll need to replace the power supply as the first action. I'm hoping the logic board is OK.
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Here's the IFIXIT guide: [https://www.ifixit.com/Guide/Mac+Mini+Mid+2011+Power+Supply+Replacement/6440] and here's the part you'll need: [https://www.ifixit.com/Store/Mac/Mac-mini-A1347-Mid-2011-Power-Supply/IF171-026-1]. To open the system you'll need to either make a tool or get this one: [https://www.ifixit.com/Store/Tools/Mac-Mini-Logic-Board-Removal-Tool/IF145-159-1] as well as the T6 & T8 Torx drivers & 2 mm Hex driver.
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The tricky part is pulling out the logic board without snagging it. Using the tool makes it a lot easier. I place my thumb on the back plate to stop it from going to far out (about 1/2") as its like a cork in a bottle you need to pull it hard but once it gives you don't want the cork puller & cork flying off ;-}
Are you able to boot it up in safe mode or under the onboard diagnostics? [https://support.apple.com/en-us/HT201255|Mac startup key combinations]. I would start there. If you can't, are you able to get it to get the system into Target Disk Mode? Let us know what works and what didn't that will give us a clue on whats needed here.