As usual there are three ways to update your DG35EC mother board bios, I use and recommend the easiest way to update the bios is to follow the Express Bios Update, its just a self extracting windows utility that makes your work simple.
The below information will give you a glance of the version no's and the operating system that are supported for Express Bios update .
English: ECG3510M.86A.0116.EB.EXE Download Directly From Intel
Ver:0116 Date:6/25/2009 Size:2367 (KB)
Operating Systems :OS Independent, Windows Vista* 32, Windows Vista* 64, Windows* XP Home Edition, Windows* XP Media Center Edition, Windows* XP Professional, Windows* XP Professional x64 Edition
If you are more enthusiastic to keep you board drivers up to date, you can try other downloads for your Intel DG35EC Mother Board Here, you can also check my previous post on how to change the bios splash screen "Change Bios Splash Screen With Intel Integrator Assistant"
Hope that helps to keep you updated!