1. Turn off the laptop by press and hold the power button until all indicators light off.
2. Release the battery. Ask we knew that the battery of this laptop installed in the case, we cannot release it without dis-assembling the case of the laptop. So to release this you should open the case, just do it because this is easy.
3. After the back case open, release the battery connector cable
4. Wait for about 5 minutes, just leave this laptop
5. Try to turn ON the laptop using the charger only, and the laptop should working right now
After all steps above done, please plug again the battery and re-assemble the back case and everything is OK.
This is the steps How to repair Toshiba S40t-A Black Screen and won't boot i hope this will help you.