Open the Network Connections folder, right click the "Local Area Connection" and select Properties. Click the Configure button beside the network adapter button. In the box that opens, select the Power Management tab and (if ticked) untick the box "Allow this device to bring the computer out of standby".
However, there may also be a "Wake on LAN" setting in the BIOS which needs to be disabled, so that traffic from the router doesn't cause the PC to boot. This is actually the more likely cause of the problem.