- Putting the firmware updater into Startup Items and control it blind
- Removing the HD and installing a bootable OS 9 with a VNC Server (for remote access) on it
- Attaching an external VGA display (not all models support that, though)
Not having installed OS X on such an ancient machine for a long time, I forgot about the firmware update requirement, and booted off the OS X Installer CD. I think you can guess what happened then. Firmware too old, no screen. So I went through the steps above and at the point of creating a bootable system with a VNC Server on it (like I have done succesfully in the past), I learned something even easier.
Start up the screen-dead iMac, let it boot into OS 9, and wait until the Finder has loaded -- you can guess that pretty well by the sound of the HD. Then push the On/Off button to put the iMac to sleep. When the green LED turns to a blinking orange, your iMac is asleep. Then wake it up with a keystroke on your keyboard and (presto!) you have your screen back!
Be aware that the display only will work until your next reboot/shutdown, so now would be a good time to run the Firmware Updater! After the update, the iMac will boot once more with a dead screen (as stated above), but after another shutdown, it will be alive again from then on. You can install OS X without any problems now. I know that the problem should be well known, but I haven't seen this simple solution anywhere on the net, so I decided to share my experience.

