After a lot of digging and consulting, pretty much all signs point to the server entering an out-of-memory scenario, causing updates that were installing to fail, leading the system into a non-bootable state. This continues to be apparent after the format/reimage as the system's available RAM has hovered roughly between 0 and 100 MBs.
I've ordered additional RAM for the server and while awaing its install I have disabled non-essential items, such as IRC. Because the system was formatted, I'm not 100% sure this is what led to what happened (as the logs that would help, if any, were lost), but this looks to be promising. I haven't heard when they'll install it yet but naturally there will be a period of downtime as the system is turned off and the RAM installed.
//A