What you need is a router that can be turned into "bridge" mode instead of "Access Point" mode. Without the exact model number of which router you have, it is hard to say if you can. Which netgear router do you have?

Even if it not a feature, many routers can use custom firmware, which can make this feature available.

I believe you do need to be running both routers in bridge mode for this to work properly. This would effectively disable any other wireless communication though. I am not sure of any consumer router that can do both access point and bridge functions at once.

Helpful questions:

- http://superuser.com/questions/19184/can-i-make-two-wireless-routers-communicate-using-the-wireless  
- http://superuser.com/questions/27720/recommended-gigabit-802-11n-routers-that-work-with-dd-wrt
- http://superuser.com/questions/672/which-routers-do-you-prefer-for-dd-wrt-or-openwrt

I am not sure that is exactly what you wanted to hear.  It is possible if the router supports it, but it comes with conditions.  The easiest solution would just to pick up a cheap wireless card for your computer in case things do not work out as planned.