OS - Operating System. You're running XP, so that's answered.
1. Try resetting the router and restarting/resetting the actual wireless connection from the laptop. Eee PCs have a hotkey to disable wireless/bluetooth.
2. Control Panel > Internet Options > Connections (Tab) > LAN Settings
Should be an "Automatically Detect Settings" box. Is it checked? If it isn't, check it and restart the wireless.
3. Click Start, then Run. Type in "cmd" and wait for the command prompt to pop up. Once up, type in the following:
ipconfig /release
ipconfig /renew
Then restart the wireless, restart the laptop, and try again.
Let me know if none of these work out.
Oh, and to download a patch, either use another computer and transfer it via a USB flash drive, or connect the Netbook to the router with an ethernet cable.