H97 and Z97 is made for desktops. If i'm not mistaken, the chipset is included in the CPU package. If you're not satisfied, you could have a look at other Core-M powered laptops on the market, to see if there's more info. Fx. Dell Latitude 13 7000 , HP Envy X2, Lenovo Yoga 3 Pro or Asus Zenbook UX305.
Have you tried using the different cables that does not work, both "front" and "back"? If they work one way but not the other, it's either a missing or bent pin in the iPhone's Lightning dock, thus you'd need a replacement lightning dock, ans Rany said. So deffinately try that.
Either the above answer by chriswku03, or it's because the units enclosure is bent out of shape. It is a pretty thin piece of aluminum after all, so it doesn't take a whole lot before its bent, especially if dropped.
If you need to replace the glass on the unit, i can imagine it's because the unit was victim to accidental damage? If so, the reason why the problem only arises when the display is seated, is because the enclosure is bent out of shape, and the new LCD panel can't handle the pressure (so to speak). I've seen this on original screens and 3rd party displays, but mostly on units with a bent enclosure, and it does not have to be a lot. The 5C display does not have a whole lot of flexibility, like the 5 and 5S, because of the extra plastic framing, i'm afraid.
Well, maybe it's his kid's iPad, and the kid put on a password and has now forgotten the password.. Nonetheless, it's none of yours or my business. Do a DFU on it, set it up as a new unit or use an iTunes or iCloud backup. But, if it's locked with Find My iPad, you'll need the proof of purchase, and contact an AASP or PSP, to get it unlocked.
If i remember correctly, the original harddrives, like in the iMac (all models previous to Late 2012), has a built-in temperature sensor that you need to account for. If the logic board can't find the sensor or the sensor gets an odd reading, the fan(s) will go haywire, to make sure that no hardware is damaged due to overheating. So if i were you, i'd install the original harddrive to see how your Mac Mini responds. If the fans operate at normal RPM's, then there you go.