
Download the latest driver from:
https://www.asus.com/uk/supportonly/Eee%20PC%201000Linux/HelpDesk_BIOS/
Rename the file to 1000.ROM or 1005P.ROM or any number that matches your Eee PC and copy that to a FAT 32 USB stick.
Start up with the USB stick inserted and hold both ALT and F2 keys pressed during startup of the Eee PC and the BIOS update will run. The screen will show the update process.