Could be the battery is dead. Today's batteries can fail after only 18 - 24 months. Try removing the battery and use the adapter alone. Most recent models can run on just the adapter.

Dell Laptop Battery - Frequently Asked Questions | Dell US

Thank you for the suggestion. I just gave this a try and had no luck. 

Hi @Momento715  the ac adapter cord that plugs into the laptop has a diagnostic LED light.
(1) Before plugging this cord into the laptop the LED should be on, to say that the ac adapter is working.
(2) After plugging this cord into the laptop the LED should be on, to say that it is supplying dc power to the laptop.
Please check that the power cord diagnostic light remains on. Thank you. 

Which model Alienware? One thing you might try is. Unplug the power from the wall. Hold down the power button for about 30 seconds. Plug the power back in and try it again. If the computer is only a month old, it's still under warranty so you could  give Alienware support a call. The couple times I have called them I always got a tech that knows what they are talking about and speak and understand English very well.

Thank you for your reply. The LED on the power cord is on before and after plugging it into the laptop. 

Hi @Momento715  thank you for sharing update.

We have established that the Laptop has a problem, but there are no diagnostic lights or beeps. 

OP says it does not Boot into Windows, but does it POST to give splash screen, and to give the F12 option to run (ePSA) Diagnostics? Or is there some other sign of life?

Please tell us more, to give a clue as to what happened just before problem and the current state of the system. 

Please click on Product Support to reveal the Revision number, if there is no revision number, the original gets the  M17x R1 designation. Thank you. 

Hi @Momento715  thank you for sharing update. 

It seems that the laptop is not getting power from the ac adapter and/or the laptop's dc power jack. 

Please check the ac adapter plug that goes into the laptop. Look inside this plug, does it have a central pin wire? If there is no wire or it is bent and pushed back out of the way, get a new ac adapter. 

Alternatively, if only the ac adapter is connected, there is a problem with the
Alienware M17x R1 Laptop DC Power Jack, Dell Part Number M6500JACK, or
Alienware M17x R3 Laptop DC Power Jack, Dell Part Number M17XR3JACK. 

Please use a bright light to shine into the laptop's power socket to determine if it has been damaged and/or there is debris that is preventing electrical connection. 

The laptop's DC Power Jack socket is soldered onto the motherboard and its replacement should not be attempted unless the appropriate soldering skills are available. This part is available from parts-people.com, and other vendors that provide M17x replacement parts. Please ensure to get the Dell part for your M17x Revision Number. 

No. It’s completely dead. It doesn’t make any noises, no fans, beeps, lights of any kind, nothing. I used it everyday for gaming for anywhere from 2-12 hours a session. It never had an issue before this. No weird crashes or anything. Always booted right up and just ran. I’ve kept up with all my updates too.