Well . . . I do not know what your situation is with regards to computers--you have one? You have 27?--but would you consider getting a newer Mac?
Or . . . have you considered getting a new logic board--ebay? Other online stores? I do not know how hard it is to replace on a Mini--Gurus can help you--but I did it on a Pismo Powerbook successfully, so it cannot be that hard!
Assuming the Geniuses diagnosed the problem . . . that will fix your Mini . . . then you can try your HD.
If it was JUST the HD, you should be able to "boot" it off an installation or various repair disks. Since I assume you cannot do that, it is probably a hardware--possibly logic board--problem.
Anyways, if you get a newer Mac, most stores will happily transfer data. Or, if you give the specs of the HD you have, a Guru here may be able to tell you how to connect it to your newer Mac to save your data.
Best of luck!
MacBookPro 2.8 GHz Intel Core i7, 16 Gig RAM, 10.8.3--"Okay . . . I will try Mountain Lion!"
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