Let's try a long shot on this one. Lets assume the router is fine as you are able to connect to this website, right?
Disconnect the cable from the WL IP. Replace it with something else.. maybe the cable is bad in the first place, not the first time a cable was toast.
Now power down your console, first put it into set up, then disconnect the AC power ( you do have the AC hooked up and running, or the electrical. it won't work on batteries with the IP).
Then remove the batteries, then remove the IP logger.
Then, put back in the IP logger, then the batteries ( it will chirp), then hook up the AC power module. take the console out of set up mode and wait for it to find your station again . You might need to make setting correct.
NOW, open your Instruction manual for the IP logger and go through step by step. However, you are going to do 2 things.. one is to use a different ethernet cable than the one that came with the weatherlink and then if you have the option, plug it into the router in a different port.
http://www.davisnet.com/product_documents/weather/manuals/07395-210_GSG_06510_6555.pdfNow if that doesn't work, then contact Davis and tell them you bought and have this IP weatherlink that is poached and you will exchange it for a new one by return mail.
Finally, is your router relatively new? I have an Actiontec Q1000 that Qwest put in years ago (I am guessing maybe 5) and it works fine, I would guess if your modem is old, then that might be a remote issue.
Give this all a try and if you have done it already, do it again...