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My seven year old laptop is shutting down within a couple minutes of booting up. I think it’s the cpu overheating because the centre top of the underside of the laptop is heating up rapidly in that time and the fan is spinning loudly. Less then six months ago I replaced the speakers and thermal paste about two weeks apart from each other (don’t think it’s fully related but just giving context). About two months ago the laptop bricked itself for a day then restarted as per normal. Then this issue appeared about three weeks ago. I’m not sure it there is anything I can do to get the system running for just a few days so I can clear the hard drive and factory reset everything. If there isn’t anything I can do is it possible to access the hard drive by removing it and accessing it via a housing unit externally?

I’m suspecting the battery and the charging logic are in trouble here given the age of your system. Lets do this, follow this guide disconnecting the battery following the first steps upto Step 6 MacBook Pro 13" Retina Display Late 2013 Battery Replacement. Now sit the system on its side with the display open so you can see it and can access the power button with nothing connected. Press the power button holding it for a good 15 secs to fully discharge the logic. Now carefully plug in your MagSafe charger your system should spontaneously startup did it? If not then your logic board is in trouble, if it does then your battery is shot. Also, make sure the MagSafe charger LED is Amber