Hi!
Usually a motherboard issue. What I would try for now, is to replace the thermal paste and get all the dust out!
If it's still having issues after this, it's most likely the CPU/GPU on the motherboard and it need a reflow/reball to get it work.
First I would try replacing the thermalpaste.
This is a teardown, but give you the idea how to get to the motherboard: PlayStation 3 Super Slim Teardown - iFixit
Please let me know how it goes and if you need anything!
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