I came upon this question a bit late. If you have no display when powering up the laptop on both the built in LCD monitor and a monitor connected to the VGA port the issue is a bit more serious.
The cause of the issue is a clogged radiator in the exhaust fan.
That being said depending on how quickly you address the issue the fix can be simple or quite complex.
Either way you will be disassembling the laptop and removing the cooling fan and heat pipe assembly from the mother board. With the assembly removed clean all the old heat-sink compound from the two (2) heat sinks on the cooling pipe assembly as well as the two (2) ICs they mount to. Disassemble the fan and with a soft brush or "canned air" completely clean the radiator fins.
If the problem is addressed right away by cleaning about 6 out of 10 machines need nothing else but reassembly with fresh heat-sink compound applied.
If the problem is not addressed right away the repair is not for the feint of heart.
To repair- After removing the heat pipe assembly mentioned above you will see the CPU an a smaller IC on the mother board. You will need to use a hot air or infra red reworking station or it's equivalent to heat the smaller IC (it is your graphics processor) to about 200- 220 degrees Celsius for two (2) to three (3) minutes to re-flow the solder connections and then reassemble as above.
All that because the fan was clogged and has heated the graphics IC enough to loosen the connections between the motherboard and the IC.
Hope this helps you fix the problem and understand why it occurs.
PC fix mantra- Clean your PC cooling system and back up your data regularly.