You've got me more confused when you start talking about voltage "out of the transformer". Typically transformers are used to step down AC voltage before it is rectified to DC in a power supply, as opposed to being used on the output? And the transformer would be inside the DC power supply/wall wart? So this makes me wonder what kind of power supply you are using in the first place? (Perhaps you are referring to the DC wall wart as the "transformer"?) A 12V AC supply would be a transformer, however, so that is why the term "transformer" raised my interest....
Looking at the schematic I see 12V going to the mosfet, as well as a gnd and the connection to the Mega. If you shorted the 12V to gnd that will drag your whole supply down, if you shorted the 12V side to the mega side that would apply 12v through r3 to the mega, not SURE if that would cause damage but I would think it could, though Bryan has said the Mega is a pretty harty chip so perhaps it would live through it. It would seem less likely that shorting the gnd to the mega would cause any damage. (not sure what two legs of the mosfet had a solder bridge?)
Speaking of solder bridges, if somewhere on your board you have a solder bridge that has a 12V line shorting to a 5V line that would push the whole 5V buss up to 12V and make it appear as though your 5V regulator is dead, if this is the case it may not be dead at all. This seems like a likely scenario to me....
If you have a digital camera shoot a picture of the front and back of your HM board and post it, with a picture we can zoom in close and look at your soldering to try and find issue, and can inspect the components to be sure they are installed in the proper orientation...
Since you are having an issue with power and have given what I consider strange details about your PS, being at 16V and something about a transformer(?), I would suggest you examine what you are using to power your HM. What kind of power supply are you using?