Any nanotech origin for the Borg comes pre-Jossed. The Borg got their nanotech from Species 149. Assuming that there numbering scheme makes any sense, that was early in their carreer but still well after they started doing their Borg thing.
I prefer the gradual transhumanist explanation, because it's so believable. Start with one small neurological implant that becomes ubiquitous due to it's utility, perhaps a wireless DNI that allows one to operate a computer and access the internet with thought alone. From there, you start adding features and designing new implants. Practically everything that the Borg has is of serious utility value to an individual. most woundly want all the implants, but many would want at least one or two. The DNI is a no-brainer, and super strength is nice, too.
Now, the problem comes in which the DNI implant starts being used for P2P chatting rather than just as a fancy keyboard and moniter. At first its no problem, because the brains remain seperate. But firmware updates that allow more inttimate mind sharing are inevitable, untill you end up mini-collective clusters, originally consisting of groups of friends, lovers, nuclear families, and workgroups. Politicians might also use it to reach a consensus more easily. But it's still very good. It's a tool, not a yoke.
Of course, it becomes fashionable to implant young children with DNI, because it aids learning and makes childrearing much easier. Young parents never have to face the frustration of not knowing what their crying baby wants, a simply mind-meld would clear everything up.
It would likely remain good for several generations. Disease isn't eleminated, but it is reduced. Violent crime is practically non-existant, as criminals would have to feel exactly what their victims felt. The network is global now, so you're linked to every other mind in the world, but that's alright, it's actually very useful. Being linked to every mind also means being linked to all the knowledge and experience of the whole. Problem solving becomes much easier.
It only becomes a problem when the children grew up linked to the Collective have children, and their children have children, and those elders who knew what it was like to be individuals died of natural causes. Over time, over the course of centuries, perhaps millennia, this society forgets individuality all together, remembering it only as a ecco of an ancient memory. That's when they become dangerous. That's what makes them Borg.