Have you removed the power and the batteries from the console yet? If not, try it.
Give it a minute or so, then put the batteries back in, then the power supply.
Then try the Weatherlink PC software program and see if it will detect the WLIP. The Weatherlink "Communications Port" option under "Setup" should identify the IP address and test it.
I had this problem in the past and the "remove power and batteries" cold-restart got it working again. Once you have it communicating again, it might be a good idea to clear the logger.
One final idea: Is the LAN port on your router auto-sensing? If not, you could try a cross-over Ethernet patch cable. Is the router already connected to a broadband modem via the WAN port? I assume that he has internet connectivity and the WLIP is actually connected to the LAN port not the WAN port.
Greg H.