More telling, we see the "attacks" in the logs even when the computers are off.
Can you spot any pattern in the IPs and times they appear?
Also, this is a long shot, but are you hosting any web pages? Big companies unleashing irresponsible crawlers can effectively DOS you without meaning to.
Further, and I know this isn't a comfortable question, but is it possible that someone in the house is logging on to certain gaming servers, and this is bringing about the attacks? If so, is there a way to get them to log in from other places?
Finally, where the hell is the NSA? Surely they're reading this thread. ;)