The machine clearly has no signs of power. Glad that warranty is there.  Contact Tech support immediately and have them replaced the motherboard.   
Inspiron 15 7506 not turning on after a normal shut down. It was working perfectly till yesterday afternoon but now it won't turn on. I have tried holding the power key for 20 sec while keeping the charger and other devices unplugged but it did not turn on. The light on charger works fine but on the laptop there is no charging light. There are no LED lights, no fan noise indicating that the system is turned on. Please help me solve this issue at the earliest. Please note that the product is in warranty. It was purchased in June this year.
Inspiron 7506 not turning