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The larger 30" displays needed a certain power level capable Mac when they were first introduced, but anything newer should be OK.Have you tested it with anything, PC or anything that has a port that would work?
Hello, yes there reason it doesn't get power is because you are without a power cable.
A kettle lead will do, but it should have had a correct cable in the box. Have you checked back there, or where ever it came from, to see if the power cable is still there?
I'm sorry I didn't see you mention you didn't have the power lead, and yes HDMI from the Mac mini will not power the display.
What is the serial number of the display? You can use that, for identification purposes.
Find out what it is by following along with this article:
http://support.apple.com/HT201864Check the information about the display by entering that serial number at this link:http://selfsolve.apple.com
The correct power adapter can be purchase from Apple if you cannot locate the original.Here's a link with more information on identifying if you have the correct power adapter:https://support.apple.com/HT201787
Here's a link to the store to find the correct power adapter for the display once you have identified the model:
If you have any problem identifying the model, or finding the correct power adapter please let me know.