From what you said, I'm assuming that the wireless network in your home is secured in one or more ways. If your wireless network is configured to "not broadcast the SSID", you might want to look at the following articles, especially the last one (which seems to have a solution for a computer trying to connect exclusively to a specific "non-broadcast" wireless network).
"Wireless Deployment Recommendations and Best Practices":http://www.microsoft.com/technet/network/wifi/wideprec.mspx
A quote from the first section ("Service Set Identifier (SSID) Suppression"):
"If you want to use SSID suppression, you should understand that Windows XP Wireless Auto Configuration will connect to the first preferred wireless network that is advertising its SSID, even though it is lower in the preferred networks list than a wireless network that is present but is not advertising its SSID. This behavior can produce confusing results when you introduce a Windows-based wireless client using Wireless Auto Configuration into a wireless environment in which some wireless networks are advertising their SSID and some are not."
"Non-broadcast Wireless Networks with Microsoft Windows": http://technet.microsoft.com/en-us/library/bb726942.aspx
"Description of the Wireless Client Update for Windows XP with Service Pack 2":http://support.microsoft.com/?kbid=917021
A quote from the "Changes for nonbroadcast networks
" section of the above article:
"The Wireless Client Update lets you configure wireless networks as broadcast networks or as nonbroadcast networks. Additionally, Wireless Auto Configuration sends probe requests only for nonbroadcast networks.
When you configure wireless networks in Windows XP, you can specify a wireless network as nonbroadcast by using the Association tab in the properties dialog box of the wireless network. To define a wireless network as nonbroadcast, select Connect even if the network is not broadcasting under Network Name (SSID)."