On the PS3, there are settings for video output. It will only output one type of video at a time, so if it's set for composite or something besides HDMI, you won't get a picture. Hold the power button for five seconds or so until you hear a beep to reset this. With HDMI connected, turn it on and it should set the video output for HDMI. Then, you choose what you want to use for audio.
Another thing is that you may have to be sure to turn on the projector before you turn on the PS3. I know it works that way with the HD-A1; if I turn that on before the projector, I get an HDMI error in the A1. I haven't tried turning the PS3 on first to see if that's the case with it, but it's possible.