Which BIOS package are you using?
In checking the TPS http://downloadmirror.intel.com/15033/eng/DQ965GF_TechProdSpec.pdf it looks like the ME is part of the BIOS file.
If it is not finding an ME when you try to update-- Not good. It kind of implies either your current BIOS image is corrupt so that the ME can not run, or your hardware has an issue so that the ME can not run.
The BIOS README file http://downloadmirror.intel.com/18158/eng/BIOS%20Update%20Readme.pdf explains how to perform a BIOS recovery which normaly bypasses a lot of the safety checks that see to it you are loading the right code on the right board or if the ME is functional.
If the ME problem is BIOS coruptiopn, recovery should fix it.
If it is hardware... not so good.
Done recovery BIOS procedure, everything works now.