The Black Screen of Death is probably just your tv/projector not getting an image from the PS3 console.
Obviously, first make sure the PS3 and television/projector are actually on.
You should then make sure all cords are firmly attached to the PS3 and you television.
If the cables are snugly in place and you still have the issue, you should make sure the PS3 is outputting the correct video. To do this, power off your system, then press the power button to turn it on, but keep it held down for a couple of seconds. It should beep and your video settings will be reset.
Still nothing? Make sure the cables are working. Swap them out with cables you know that work, or test the cables in question on something else (another PS3 or old PS2 for the regular cable, anything that has HDMI out for the HDMI cable).
Really? You still have the issue? Okay, maybe the problem is more serious than previous thought. You might have to send it in to Sony, which can be done
here. They take forever to send it back though, and if you're out of warranty it costs $150 (it's free if you're under warranty though!).
Alternatively, if you're awesome and feeling adventurous, you can fix it yourself.
Here's a guide, and more can be found online.
Regardless, hope everything works out!