For those wondering, who maybe have the same issue, I stumbled upon a fix today. Don't know whether it's permanent or temporary, but my computer is uploading now, and sites are working as normal on the network. Yes!
I have a Wacom tablet that was playing up, so I worked to get it working normally again, including uninstalling and reinstalling the programs and the drivers. I'm guessing that somehow this software was messing with my connection to the network, but I'm still not sure how. In any case, it's resolved now after a few months of trying to figure things out. Hopefully this is of some help to someone!