The drivers you mentioned are very old. Please try updating to latest driver by downloading it at this link:
As part of the troubleshooting steps, testing another Cable may do the trick.
The drivers I originally installed are the latest Asus provided ones.
I've just uninstalled it, and installed the generic Intel one you provided in the link (18.104.22.168.3958), but the problem still occurs....
the screen turns off after the windows starting message, prior to the windows logon screen being displayed.
I'll get hold of a new HDMI cable and retest it tonight, but I doubt that will make a difference since neither the monitor on the HDMI nor the monitor on the DVI are currently working when using the Intel driver anymore (and were without a problem previously), and they both work correctly using the built in Windows VGA driver.
I've tried it again with a different HDMI cable, but there is still no display using the Intel driver, but the default VGA driver works fine.
(Removed the 2nd monitor and the DVI cable too, to ensure that wasn't impacting it in any way).
This seems very strange since the Intel Driver seem faulty, but it was working correctly previously for more than a year.