If the display is the problem, it is possible that is why it is shutting back down. However if you can't see what is on the display (error, etc.) then you can't know. You can try the following, to see if you can at least see any error messages, however should that not work, I would suggest having the laptop looked at by a tech.
Try this...
1. Turn the laptop off (not sleep or hibernate but off).
2. Connect an external monitor to the laptop.
3. Turn on the external monitor.
4. Turn on the laptop.
NOTE: You may have to press an "external monitor" button. Could be the f4 button or a button with two monitors on it, for the external monitor to work.