How to Troubleshot WiFi, Wireless Network: When You are not able to See the Network in Scan List on Client

Well your problem is about Routing Table.

Give us some more detailed info about your Router.
Manufacturer: Linksys, ASUS, Etc.
Model:
Networking Scenario: Your router itself connected to Internet or its connected with other ADSL, Cable Modem?

Do these simple steps to troubleshoot wireless connectivity

1- Login to your router Configuration page ( Most cases this is http://192.168.1.1)
2- Remove all security settings, WEP, WAP Etc.
3- Go to the Network Setting page and Add New Route. 192.168.2.1
4: Now if DHCP is enabled fine, otherwise you have to configure you Computer TCP/IP settings again to use this router as Gateway. ( IP : 192.168.2.* Subnet: 255.255.255.0 Gateway: 192.168.2.1 ) Where * is anything between 2 to 253.

Hope this would resolve your issue.
Many peoples who are new to Networking get stuck over this point. Your default route of router is 192.168.1.1 and its already busy and connected with your modem so you can't use it for your system connectivity for internet surfing. There you have to add a new route for your wireless Networks (WLAN ) or even for local area Networks (LAN),

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Editing: Adding

One more problem is possible while you can not see your Wireless Network in Windows XP ,

2.4GHz Wireless network could be one of the following.

1- 802.11a
2- 802.11b
3- 802.11g (Have Back end Connectivity for 11b)
4- 802.11n (Latest) (Have Back End Connectivity support for 11b, 11g)

Your Access Point or Wireless Router is configured to use 802.11n
Your Wireless adapter in Windows XP is configured for 802.11b Connectivity.

Now if your Access Point is not configured to use back end support for 802.11g & 802.11b then your Wireless adapter in Windows XP would not be able to find that network.

If Your Wireless Access Point or Router is configured to Force connectivity to 802.11g then your client supporting 802.11b would not able to see or connect the network.

Thanks.