Oh wow, you've got to be kidding me! I can't believe it's doing that already. You know what I would honestly do? Every computer is covered under warranty no matter if you purchased an additional warranty in the store you bought it or not. I would take the Asus back and demand them to either swap it out for the same one, or give you your money back. Some places will want to "send it off for repairs" make sure you stress that you are not waiting for them to send it off, you need your computer for work and can not have any down time.
I've been a tech for many years and have seen some terrible quality control checks with all computer manufacturers. From the symptoms you are describing there is only two things it would be now. Either the AC adapter for some strange reason has decided to go faulty, or a stick of ram has gone bad in the all-in-one.
A blinking light indicates a hardware/power issue.
This is outragious that it has only been under a month and your in a situation like this.
I'll tell you what, let me know what happens when you take this back, i'll be here to help you in any way I can. If they need it to be "checked out" by a tech before the swap or replace it please let me know and i'll write a report for you that I have diagnosed it.
If you have a moment don't forget to rate my help below (an excellent service rating
is most appreciated)
(To rate my help click the smiley faces below
then press the submit
Also if you need any computer help in the future no matter what the issue is, you can return to this chat anytime day or night (I am online from 9am est until at least 11pm est every day of the week)
Thanks again for all you patience