Today I finally solved the myth. It has something to do with the setup of my wireless router. Previous I set the "Authentication Type" to "WPA-PSK", and set the "Cipher Type" to "AES". I found that Windows XP only supports "TKIP" as the "Cipher Type" (Control Panel -> Network Connections -> Wireless Network Connections -> right click -> Properties -> "Wireless Networks" -> choose your home network -> Properties -> Data Encryption. You'll find only "TKIP" in the drop-down list.). Therefore I changed the "Cipher Type" in my wireless router from "AES" to "TKIP", and bingo, my Windows XP desktop connected to the network immediately. My Windows 7 desktop connects to the wireless network much faster too.
I think this is because the wireless adapters in my desktops can't handle AES encryption very well, but the new laptop doesn't have this problem.
It turns out that TKIP usually goes with WPA, while AES usually goes with WPA2. The latter has better security than the former. (http://www.openxtra.co.uk/articles/wpa-vs-80211i)