I got an Alienware x51 at the beginning of the 2012 summer. I quickly noticed that whenever I watched Youtube on fullscreen and many other things, there was a high chance of my computer freezing up. The screen would be frozen and would give the youtube video a blue and red effect. I'm not sure exactly what was going on, but the only option was to reboot it to make it stop. It stopped doing this for months, but I just got the same problem again yesterday. If anybody knows the cause of this problem, please let me know. The screen would freeze to whatever frame of the video I was on, but it would get a really distorted effect with blue and red all over the place. Nothing would respond after that.
My graphics card is an Nvidia Geforce GTX555
Since the computer is still in warranty I'll recommend you get it fixed by Alienware service centre itself.
Otherwise this can be a ram issue or an overheat issue.
Reset the bios and see of it fixes the problem.
Monitor the temperatures and make sure the temperatures are not too high under load.