Start your ps3 with a hard video reset (turn on with finger until you hear the beep after the initial beep) make sure both cables are plugged in at same time. AV and HDMI.
Set the channel to HDMI while doing this. Wait for about 30 seconds after the beep to see if it shows anything. If it doesn't then switch to AV. If on AV it says an HDMI cable has been connected, even though it didn't show... the HDMI controller chip on the motherboard is bad. If it boots straight to AV and doesn't recognize hdmi was there. Then either the port is physically broken or any number of small components on the MB relating to the hdmi pathway could be bad.
I fix these issues on a daily basis at work.