I am not sure what you mean by "4-port Belkin router is seing two network cards on my system", unless the router has ir capability. Routers will only know what's connected to them, physically or wireless (wireless is differnet than ir). I have an ir device,lan card and pcmia wireless card on my laptop and all are enabled but my router doesn't see the ir device, or lan card. It only sees the one connected to it (the wireless in my case) But, as you look in the Network properties you see all the adapters installed on your computer. You should see a listing of your Infared adapter (the one with the netcard icon next to it), look at the properties. Click on the Bindings tab. Make sure the infrared protocol is checked. Now look at your netcard (ethernet) adapter properties. Again click on the Bindings tab. You should see choices here: make sure infrared protocol is not seletcted. If it is selected, your telling your computer to use the infrared through your netcard as well. This could be the reason why the router sees two connections. Two devices are sharing one device through two different protocols. Conclusion- make sure the ir is bound to the infrared protocol and not your netcard and vice versa.
I hope this helps