Hi!
To be honest, this could be caused by multiple components.
Could be caused by the Sony CXM4027R MultiAV driver IC (this one does fail sometimes and is communicating with the HDMI signal).
Could also be the Panasonic MN8647091 HDMI transmitter IC.
It's also possible that a fuse/capacitor need to be replaced to get it working again.
For now it's for the best to open the console and check the motherboard.
All of them requires soldering plus soldering skills to get the PS3 fixed.
Here is the guide so you can determine to do it by yourself or let someone/shop to get it fixed for you.
[guide|10670] (step 14).
Good luck with the repair and please let us know how it goes!