One thing I tried that got me attention was when the tech support guy picked up, I gave them the necessart info and when they asked how they can help me, this is what I said:
"I have a 19" <insert model here>, this is the 3rd one I have recieved from you in this <put months/years here> time. I just checked the cables, tried different cables, did the self test and did the reset. I have tried it on another computer on which the video card works guaranteed and got the same problem (even though I didn't run any such test), I have tried a friends monitor on my pc and it works fine (this I did do). If you will notice this is the 3rd one you have sent me so, I'll give you a minute to check if you want. Please do not waste my time, I want to speak to a manager, someone who will give me a refund or an upgrade."
That is pretty much what I said, calmly but firmly. The guy started with the "we can't do this/that" I said "I know you can't that is why I asked you to put me on the phone with your manager." Personally, when I was having to call up 2 months after getting the replacement that my 3rd monitor wasn't turning on after I got back from class, I was pissed, really pissed. I pushed and pushed for 10 mins with the manager for a refund. Told him I spent $400 on it cause of what I had heard from friends and cause it had a sony trinitron tube and this is not what I expect, to have to waste my time on the phone for something I spent all this money on. After 10 mins of telling me that he can't give me a refund I asked what he could do, and he gave me an upgrade.
I guess the key (which I'm sure you're aware) is to stay calm and composed at all times. I'm sure he knew I was pissed, and I did let him know I wasn't happy, but never gave a hint of anger. Oh, another thing I bought up was loss of productivity, kept saying that no monitor means that I can't do my work (I hinted I do some big job related work on this monitor).
Hope that helps. Sorry if its a lot to read, I'm off to bed now though. Best of luck.