You could return the system to Walmart as they have a 30 day return policy. I suspect if you call Dell and explain the situation to Customer Service, and have the receipt then you should get warranty service. But lets try the easiest procedure which is a reset. Remove the battery and unplug the adapter. Then press and hold down the power button for 30 seconds. Now reinstall the battery and plug in the adapter. Try to restart the system. If that does not help then have a look at the RAM and make sure it is seated properly, it may be a good idea to remove the RAM and reinstall it. The service manual is here with all the directions described.

One question, are you hearing any beeps or seeing any flashing lights?

Walmart USA return policy is as follows here.

Hello!

I'll be sure to try that idea! 

The reset and ram suggestions didn't work.. 

Yes, I am! I hear a beep when the laptop shuts off, and sometimes when I attempt to turn it on, the caps lock LED flashes once really fast! 

I got an answer on another website saying that it may be a problem with the motherboard? 

https://www.ifixit.com/Answers/View/608425/New+Dell+Latitude+E6440+Won't+Power+On#answer608441

Hi,

you posted a link should we be using ifixit.com to resolve issues?  I also have a E6440 and need to address an issue with Power.

Thank you,

Jim