I had a Toshiba Satellite C50-B (p/n: PSCLVA-002001) which switch off itself after 1 minute. The power light and CPU fan stays on for a bit, but then switch itselfs off. It's not an overheating issue though.

Original issue was the screen stays black with a bit of light after switching it on. The computer stays on and accessible via Teamviewer. Display also shows if you connect an external monitor to the laptop via HDMI port.

The switching off started happening after I removed the battery.

I then dismantled the screen and reconnected the video cable which made the screen to work again. It turns out the cause of the switching off is because of the video cable connector.