A failing NIC can flood the network with packets and cause chaos. As can a failing DHCP server.
If you suspect a particular NIC, remove it form the network for a short while and see if the problem resolves, then reintroduce it and see what happens. If it's the router, the only solution is to try another one and see if it helps.
Still wonder about trojans though. Did you try Symantec's online check? It's definitely up-to-date.
Cheers
Mick