Alienware 14 AC Adapter Won't Recognize

Hello! I'm having a weird problem. 

With a brand new AC Adapter (just replaced the old one, and I've confirmed that this one works on another laptop), my Alienware 14 behaves as if the AC Adapter is unrecognized. It doesn't give me any kind of message about it. The power button even changes color when the AC Adapter gets plugged in, although it won't change to the color that indicates charging. And when I unplug it, it turns orange/yellow, the color that indicates it is unplugged. But on the bottom right, the computer stays on battery power-- as if nothing is plugged in at all! 

I thought perhaps it may be a software problem, so I did a master reset, which didn't fix the problem. Unfortunately, the laptop has just now died, so now I'm using an old one. 

If I unscrew the laptop, take the battery out, hold the power button for 10 seconds, then put everything back in and replug everything, do you think I have any hope of fixing it? And if not, how do I go about getting this fixed? Do I contact Dell? I bought the laptop originally from Amazon I believe, possibly from a third party seller, although it wasn't used and has worked just fine for over a year.