Woah! You edited your question completely on me!
Here's my original answer:
-------Are you looking to connect the two routers wirelessly or through a network cable? Only some routers support this "bridging" function. Or you can buy a "range extender". Basically the router is working as a "dumb unit". That means that it doesn't do any network processing, only repeats what the original router has done.
This function isn't very common in router, so chance are, if you have two routers, you've got about a 20% chance of having one that has this functionality. If by chance you do have one that supports bridging, they can usually repeat the signal wirelessly or connect to an Ethernet connection.
Your best bet, honestly, is to spend $20-$30 on a wireless NIC.-----
New answer: yes, if you have a legacy PCI port, that should work fine... But that card IS NOT wireless.