While there is a newer driver in Windows Update, you can't reach it without an installed driver. An alternative to the XP 1.19 driver is to use another machine to go to Windows Update Catalog (
http://go.microsoft.com/fwlink/?LinkID=8973) and search for "SIS 900". There you'll see the drivers listed 4 times (different languages and CPU architectures, but the description appears the same). They're pretty small so add all 4 to your basket and download them. Then look at the filenames to determine which driver you want - they're in .CAB files which you'll need to extract first (Window Explorer should be able to handle them).
Copy the extracted drivers to a CD/USB Stick/Floppy etc. then transfer them to your Win7 machine. Right-click on "Computer" and select Manage. Go to the Device Manager and double click on the non-working network card. Click Update Driver. Choose to specify a location on your machine. Point to the folder where you copied the drivers to. They should now install and the network card should start working.
Enjoy!
Rob