Typically this means that the GPU has become unsoldered.
Your absolute best bet would be to call sony to ask them to repair it since it's a semi-common problem with older PS3's. Obviously though since you're probably out of warranty there'll be a fee, about $100 iirc.
You might could look into a non-sony repair group if you're not willing to spend that much but I wouldn't guarantee anything.
If you don't know how to fix it by yourself, I must implore you not to try it. DIY fixes have often disastrous results.