You're going about this the wrong way. What you want to get is a wireless repeater/relay. Something that will pick up your neighbor's signal, and then amplify it so that other devices can pick it up.
Good news for you, is that you already have all the hardware you should need, but you'll have to flash a custom firmware onto your router known as DD-WRT. It should let you configure the router as a client instead of an access point, so as long as it can pick up the neighbor's signal, it can then act like a shared wireless card to any device connected to it. The one drawback here is that both systems will have to be connected via an ethernet cable. You'll be losing your own wireless ability unless you want to buy another wireless router and connect THAT to the 160N with DD-WRT.
Trying to set up connection sharing like you were talking about would be a nightmare. Many have tried, and given up. The few that succeed are pretty much universally disappointed with the results.
I have a laptop and desktop both running Windows 7 (Ultimate on the desktop and home premium on the laptop) and a Linksys WRT 160N wireless router. I also have a 4 port hub if needed.
I am picking up a wireless internet signal on the laptop from a neighbor with their permission. What I'm trying to do is provide internet access TO my desktop FROM the laptop. I tried to use a wireless network card for the desktop to try to do this directly, but the signal was too weak. I'd rather not shell out more money for a card with a good enough antenna but just find a way to utilize the internet that the laptop is able to pick up well.
Does anyone have any ideas?