Hi,
Please do try these troubleshooting steps that may help.
- First is to do a hard reboot, remove the battery and unplug the AC adapter then press and hold the power button for 20 seconds then try booting it up again.
- If it will still shutdown by itself, remove the battery again then connect the AC adapter and see if it will stay on or boot up normally.
- If the same problem will persist, do try a different AC adapter and see if it will work or not.
- And if that will still not work, I would suggest contacting Toshiba support if it's still under the factory warranty for a repair.