When you power on the system, does it stay powered on all time or does it go off automatically? What is the status of the keyboard leds - caps lock / num lock / scroll lock pattern? Do the fans come on and stay on?
Disconnect the adapter and battery and press and hold the power button for 30 seconds to release any static power. Then try connecting with the adapter only / battery only.
Press and hold the fn key + power button to turn on the system and it should initiate the diagnostics - check for any possible beep codes.
Run the LCD bist - Turn off the system and press and hold the "D" key + power button to turn on the system and it should run the LCD built in self test - see this link for more info - http://dell.to/1SkXNrG
Download the service manual here - http://dell.to/2kgaDxi - remove the HDD / ODD / memory and try powering on the system.
If nothing works, then I would suspect a motherboard fault.
You could contact our team to get a quote for a paid service call - http://dell.to/1vnT6CQ
You could also order the parts online here - http://bit.ly/2jmDMa2
Also, please click my DELL-username and write me a private conversation with the service tag and your contact details(Name and Email) for case records.
Let us know if you have any other queries.