I'm sorry but I don't want ANY link between Humans and the Borg when it comes to their origin. I just want the Borg to be completely separate.
The Borg were around 900 years before Voyager and by that time controlled only a handful of sectors. So we know they basically started to "spread out" 900 years before Voyager and were already in their cybernetic form by that time. The Borg Queen also mentions that Humans are not that different from the Borg before they became what they are.
This all leads me to believe that perhaps the Borg pre-cybernetic were like Humans, they warred with each other and perhaps began developing weapons to try and win the other which lead to the development of the nano-probes and cybernetic enhancements for their soldiers.
Clearly something went wrong, perhaps the scientists on the otherside of the war reprogrammed them into a viral weapon and thought they would wipe out their enemy which backfired and ended up spreading throughout the entire populace. In all the chaos this new Borg species generated a Queen to bring order and the Borg began from there.