Microsoft Wireless Broadband Router

I’m fairly new at networking. I just bought Microsoft’s Wireless Broadband Router and did the typical installation to my mother’s computer which is wired to the router, wired to a cable modem. I have a Built-in Wireless LAN (802.11b)device on my Fujitsu Lifebook P2120 with Windows XP home edition. I was able to figure out how to get connected to the internet but it seems that I have to have my mom’s computer on the access the internet. Is it possible to connect when my mom’s computer is off. She has a big thing about not leaving the computer on when it’s not used. So, can anybody help me or did I throw over a hundred dollars down the toilet? Any help would be appreciated. Thanks.