Alienware 14 not powering on

I just received my Alienware 14 on 04/21/2014 and on 04/25/2014 it suddenly powered off on me. I was no longer able to turn it on at all. I called Technical Support and they helped me trouble shoot the problem. They told me to plug only the adapter into an outlet to see if it was working, which it was because the blue ring on the adapter did light up. Then as instructed, I plugged the adapter back into the laptop and the blue ring turned suddenly turned off. Technical Support told me that either my graphics card or motherboard had short circuited and that I either can have it fixed or replaced. I was worried that it would become a hassle to have it fixed and come back with the same issue or a hassle to have to almost wait another month to receive a replacement, so I just requested to return it for a refund.

Now, I am wondering: Will I get charged the restocking fee for returning it? I read in the return policy that I would not be charged if the product was defective.