After trying 50 or so times, the rig booted! But only to the "Starting Windows..." screen, then it hung.
Considering it's a mining rig, the video card is most likely fried--as opposed to being a m/b or psu issue. PSU and motherboard issues tend to result in random or frequent reboots. What it sounds like is happening here is that as soon as 3D acceleration drivers get loaded, the card is taking a dump. I think the VGA port still bypasses any fancy chips until those drivers are loaded, whereas DVI/HDMI probably don't, and this might be the reason why you were able to get further using that port. Although since it has only "worked" once, it is still pretty likely that the card is in a real bad way.