Are you sure it's a router that's connected to the cablemodem? If it's a switch or a hub... or if you're calling the cablemodem itself a router... then we have an entirely different situation here. I bring this up because you mention a specific make and model for the computer, which probably won't be the least bit relevant, but you don't mention the make or model number of what you call the router, and you don't even mention the cablemodem.
Such inconsistency in details raise big red flags because that says to me that no or little attention was paid to the parts that weren't described in detail, and that raises the probability that the problem will be found where little or not attention was paid.