From Dell
http://www.dell.com/support/article/uk/en/ukbsdt1/sln298524/how-to-use-and-troubleshoot-the-inspiron-17--5759-?lang=en#Computer_Fails_to_Start
11. The Computer Fails to Start or There is No Video
If you experience a situation in which the computer does not start at all or if it does turn on (lights turn on and fans are spinning), but the computer does not show any image, perform the following steps.
Disconnect all external peripherals including the keyboard, mouse, and external monitor. Peripherals also include external storage devices such as flash drives, USB devices, printers, cards etc.
Remove the A/C adapter from the computer and unplug the adapter from the A/C outlet.
Remove the battery, for more information on how to remove the battery, browse to the Inspiron 17 (5759) Online Manual Page, click PDF next to Service Manual.
Press the Power button for 15 seconds.
Make sure the connections on the power cord and A/C adapter are firmly pressed together.
Insert the A/C into the computer and a good A/C outlet.
Press the power button to see if the computer turns on and boots up ok, if not, refer to Dell Knowledge Base article Computer Does Not Turn on, or is Stuck on the Dell Logo Screen.
Turn the computer off and insert the battery back into the computer.
Press the power button to see if the computer turns on and boots up ok, if not, refer to Dell Knowledge Base article Check the Battery.
Start attaching devices one at a time and testing to see if the computer will turn on.
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