You may have to pull the battery (yes it may be hard to get to) and remove the charger cord to get it to shut down if it is frozen.
Once you have it shut down, connect an external monitor to the laptop. Then turn on the external monitor and finally turn on the laptop. If you can see the screens on the laptop, then your attached display is your problem. You would need to check the ribbon cable for it to see if it is loose, damaged, etc., and if it isn't then the display itself may be the problem.
Now if you can't see anything on the external monitor either, but you are sure the laptop turned on, then your graphics card/GPU is probably done for and will need replacing (which may require the motherboard be replaced).
NOTE: If your laptop is still under warranty, do not open it up or do any physical work to it. In that case you should contact the manufacturer.