Ois: 1) Despite explaining issues on the phone, I've had the person on the other end still go through a series of 'tests' they want first ... No response after powering on, no POST, no lights, no sound (beeping, whirring, buzzing, whatever!), nothing: Try a different monitor was the answer.
Ah, that's always fun. :)
My favourite memory of this sort of thing is when my router bricked during a firmware update and the Telecom support guy wanted me to try plugging it in to the wall in another house. Not only would this obviously not get a different outcome I had clearly described to him the distinctive top-and-bottom light arrangement which it didn't display at any time during normal operation (I suspect these lights are mentioned in the manual as its equivalent of the RROD).
It was partly my fault for trying to update their rubbish custom firmware--a feat I wisely never attempted again--but I was surprised that they didn't seem to have any information on hand about something as basic as fault lights for a product they were selling by the thousands to all their broadband subscribers.
Having ISP support consistently insist on walking through double-checking each and every step of the configuration whenever you ring up to find out what the dialup number or SMTP server is is a close second though. :D