Super slim PS3s do not show a yellow light or blinking red light, they just shut off after being turned on, which is what your console is doing. This is likely being caused by a problem with the GPU on your PS3. I would suggest attempting a re-flow on the RSX chip. If that does not work, you may need to get a new PS3. 15.
The slim doesn't easily overheat, the main cause is that the cooler and fan is clogged up with dust making it very difficult for it to stay cool. Take a look at some YouTube tutorials for opening up the console and give it a full clean. Do an internal cleaning especially the fan. And replace the thermal paste.
Just simply unplug the PS3 slim from the power outlet, then hold down the eject button, and plug in the power cord it will cause the fans to whirl at their highest settings to blow out the dust. After that, use can air, then once you blow more dust out, you repeat the fan test.
Play PSP, PS1 and PS3 backups off internal or external HDDs. Play PS2 backups off internal HDD. Manually install PKGs of games, apps and homebrew. Use Multiman, Irisman, Webman. Use Retroarch. It is not as robust as a true CFW but it gets the job done and checks the majority of boxes that you would care about.
WWkFuqA.