The 1306 thing in your network connections will be your firewire card. For some stupid reason, Windows bundles this with the networking stuff (it can be used for networking, but usually isn't).
Not to jump in on AC's answer, but I would suggest doing the following:
1) Turn off all stuff. Then turn on router, followed by your machine (ideally connected with a cable, not wifi), in that order, and waiting for a few minutes between.
2) Goto the command prompt (on XP it's start->run, type "cmd", then in the black window that appears type "ipconfig /all". (no quotes).
What information does it give? (copy all of it to here.)
What is the brand and model of router?
When you connect router to PC via ethernet cable, do lights turn on and/or flash on the back of router and/or your PC?