Our home has a wireless network set up, but unfortunately an Xbox wireless adapter costs $100. There is a computer near the Xbox that is connected to the wireless network using a Wireless-G PCI Adapter with RangeBooster. I want to be able to share that connection between the Xbox and computer, but I can't enable Internet Connection Sharing. An ethernet cable from the PC to the Xbox has not worked, as it says it cannot acquire the IP address. Any ideas?

wire the xbox to the wireless router ,not the pc.

This is confusing to me, because I'm not exactly sure where the router is then. The rangebooster is just a chip in the computer, with no other ethernet port. So can the computer become a router?

Our home has a wireless network set up,

you say you have a wireless network setup ,in order to have this you would have to have a wireless router ,hooked to you inter modem,and the computer with the Wireless-G PCI Adapter with RangeBooster in will be picking up its signal from you wireless router .or wired to the modem and is not using the Wireless-G PCI Adapter with RangeBooster.
wireless route would look something like this .
http://sanantonio.craigslist.org/sys/515166164.html

So can the computer become a router?

No

its 5:45am and im off to work soon and will not return until 7pm