System starts, but nothing appears on screen.

If you have the option to send this in for warranty, I would absolutely take advantage of that since the fix is not terribly fun to do. The one I hope you only have to do is a soft reset of the video which involves you holding the power button for 8 seconds or until you here the beeps after the initial power beep. This will power on the system and after you hear the beeps you let go and it will have reset the video to factory defaults. From there select the appropriate video setting for your television and while you are at it get a can of air and try to clean the dust out from the fan on the bottom and make sure there is good air flow from the back of the system. If you are able to do this do not continue to read this answer.

You are still reading? Well thats a shame because it seems like this a problem with the GPU thinking that it is constantly overheating and shuts itself off to prevent any further damage. The only option you have is to disassemble the system and overheat the GPU and surrounding memory chips to try to get the GPU to reset itself. The article for the YLOD fix applies to this solution and is very good, but as a personal note, DO NOT move the board during and 10 minutes after using the heat gun or you could permanently damage the motherboard, and a replacement motherboard should not be purchase as it is married to the blu-ray drive so if either are swapped without spoofing then you will no longer be able to read any disks.

I have included the link to the repair guide here.

As a side note, it is important to maintain good air flow after repairing the device. If you do not then you might have to do this repair again in a month or two.