We see them in need of cleaning (heatsinks, vents), dead fans and a few where the internal heatsink has lifted off the CPU. Given the age this may be proper since very few get the needed service.
Tell us about how you clean the machine out, check the fans and see if the heatsink is on proper.
Just this morning, after trying to power up my Toshiba after I shut it off last night, but after plugging it in to power, it fires up, takes me to my Windows sign-on account screen, allows me to sign on, powers up to give me my desktop, but within moments, it automatically shuts down (a complete power down).
So I reboot it and the same scenario happens again and again. Sometimes it will give me about 30-seconds after my destop is displayed, sometimes it shuts down even before the desktop is completely settled (when hourglass disappears).