It seems like your drives are getting damaged. The question mark icon means that your system software cannot be found/loaded, and that means the system software and possibly the drive has been corrupted. I would definitely get a copy of Disk Warrior if it hasn't been used before. The globe icon simply means that the machine is looking for a NetBoot system folder to boot off. The machine will continue to look for many minutes, and then it will look for other volumes to boot off. This usually happens when nothing has been selected in the Startup Disk control panel, and that may happen after an OS reinstallation. It may also happen if no system software is found locally. Go to Apple: Control Panels: Startup Disk and select your boot hard drive to fix that issue.
The original poster stated that the machines go in for regular repair, and if that's the case they're either being repaired poorly or there are hardware problems involved. If you listed what was done to repair the Macs, I would have a more complete profile with which to work. Finally, I'm not too sure about your monitor problem, but if these are CRT iMacs, you may be suffering from the A/V board issue. That is a hardware problem. You may need to send the affected machines in for true servicing, because it doesn't sound like the service you've been getting is all that great. Macs shouldn't be malfunctioning the way you describe.