Alienware 18 shut down and won't power on; power brick's green light turns off when plugged into the laptop.

I'm not particularly savvy with hardware, so If I'm leaving any need-to-knows out, I'd appreciate if it was made known.

I have a year-old Alienware 18 bought from ebay at April 23, 2014. The warranty expired on April 23 of this year.

While I was in the middle of running a game, the system shut down, and I could not get it to turn on again. I thought it was a power issue at first, so I checked the power brick and saw that the green light was off.

Upon testing around a bit, I noticed that the light would only turn off whenever plugged into the system itself. Unplugged from the laptop, the green light would remain on.

Upon looking around at previous issues, it seems I might have a faulty motherboard.

I want to know how to confirm this, and if so, what steps I should take to begin fixing this problem.

Thanks in advance.