I extracted the BIOS chip, erased & reflashed (& verified) it externally with Buspirate, using a .bin image I retrieved, put it back in place, reset all settings, disabled boot from all external devices, etc. but the problem is still there.
As the .bin file has the previous BIOS version, I then tried to apply the latest version from Windows .exe, and it still fails to update the ME part of the f/w (rest of the f/w components are updated just fine).