NOTE: This answer would void any warranty
A very common problem with PS3 consoles (especially after years of use) is that they start overheating. This can cause multiple problems, among them are video issues due to failing solder joints near the GPU.
The reason this happens is over a course of time, the solder holding critical components on the Playstation (in your case the GPU), becomes cracked and damaged from regular use. This problem is also more prominent in Playstations that were not given enough room to vent while running, but can happen to all of them.
Since I had the same issue (and used to do professional hardware repair of Video Game consoles) I am fairly confident that a 're-flow of solder' would fix your issue. But it is VERY involved and not for everyone. (i.e. you may just want to buy a PS4 or another PS3 instead)
In order to re-flow the solder you would need the following:
- Industrial Heat Gun (to heat solder to melting point)
- Lead-free Flux (to 're-flow' the solder and fix damaged solder joints)
- Various tools to take apart the Playstation 3 (most of which are security torx bits)
NOTE: It is also recommended to have an IR temperature gun to ensure
the processors themselves are not getting too hot while re-flowing
As a quick idea of what you would need to do:
- Take the Playstation 3 COMPLETELY appart
- Apply flux near solder joints at the GPU, CPU and any other places where you suspect there may be damage (Doing a majority of the system board is recommended)
- Use the heat gun to heat the solder points until they are 'shiny' and 'melting'. If you got the IR temperature gun too, be sure to monitor the processors according to the Playstation 3 tech specs (which if I find again, I will update this post to include them)
- Wait for solder to solidify again (wont take but a few seconds after removing heat) and put your Playstation back together.
As I said, I have done the above process on many Playstations with VERY similar issues. I hope this can either help you, or at least provide some guidance on what might need to be done if all other options have failed to fix your issues.
As another note, if you do plan on getting another PS3 and don't want to lose your games (and if your Playstation is still working enough to do it) be sure to back up all your games in a manner you can restore them to the new Playstation. Since you can't just take the existing Hard Drive out of the old one and put it into the new one without issues.