Welcome to the Community. Is there a light on the AC adapter ( Charger ) when connected to the system? Do you hear any beep codes. There are 4 LEDs in front of your system, ( Power light, Wifi light, hard drive light, battery light ) which one of them are off/on/blinking ? Remove the battery and the ac adapter, press and hold the power button for 15 seconds, and connect the AC adapter alone to check if it powers on.
If it still does not power on, you will need to start reseating a few components on your computer, like the memory, hard drive, wireless cards, optical drive. Use the below link for help.
I have 2 Dell Inspiron laptops that will not turn on at all. Just purchased new batteries for both, both power cord lights are on, no lights on the front of either laptop & upon hitting the power button lights in the top right corner come on for maybe 3-5 seconds then nothing. Have tried to take battery out & hold power button to drain. Nothing at all happens with just the power cord but the lights do flash with the batteries in. Both are just over 2 years old. Both happen within the last week.
sorry both are N7110 Dell Inspiron