This is so weird because I just had this happen to me, too. I have the same system and it worked fine Friday night. I turn it on Saturday morning and nothing... the lights turn on, the fans start up, but nothing else. No video, no sound of windows loading, nothing. I also got the on-site warrenty and the computer isn't even a year old until August.
I called tech support and requested someone to come fix it. Nope, can't do that. They wanted me to open it up and figure out what the problem was myself and then they would see if it required someone to replace a part, which is all the on-site service does. On-site service does not include trouble-shooting they told me.
I explained that I'm not a computer tech and if it were my car that was having problems, I would take it to a person that is qualified to determine what is wrong with it. I wouldn't do that myself.
So anyways, my computer is now on it's way to Miami. This is my second Alienware. My first one was fine while under warranty, but now 1 month after the warranty has expired, it's having heat problems. I won't be buying another Alienware, that's for sure.