It appears there's a video-detect reset function of the PS3. Assuming there's no hardware trouble, the cables are all connected properly, and the TV is set to the correct input, try holding down the power button for 5 seconds or so while the unit is off. It should beep a second time to let you know it worked. Now, try turning it on.
It also appears that Tim Gelvin (iFixit contributor) is [guide|5163|writing a guide] to address this exact issue. It's showing up as incomplete, but it helps to validate my own research.
I hope this helps!