Sorry, don't mean to ask the "dumb" question, but how did you hold down the button? You have to turn it on by holding down the power button until it beeps the second time to clear the audio and video settings.
If that's not working hook up the PS3 to both your old display ( using whatever cables you were before, ) and your new one with the HDMI. Turn on both displays and the PS3 ( so you should be seeing it on the old display, ) then change the video settings over to HDMI. The screen should flash and then transfer over to the new display to confirm the change.
It's also possible the HDMI cable is bad.