Why I ask is that in my state the warranty is extended by the number of days the machine was out of your hands.
Also check if the purchase was by credit card as some CC's extend warranties.
As to what else to try, another power cord. Sadly it sounds like a hardware failure. That is something needs replacing.
Thanks for the full model number. It leads me to want to check the power brick.
https://www.google.com/search?q=C1A73AV seems to be it. A good tech can use a Volt meter to see if that's it.
Figure 50 to 100 for the brick.
My TouchSmart shut down friday night as I was browsing the web. It was plugged into a brand new surge protector, and it would not work when I tried to turn it on again. After Googling online about the issue, I tried the 30 second pressing the power button method. I also tried to move the computer to different rooms and turn it on. Nothing. When I turn it on it doesnt light up. And the back nor the adapter lights up when I plug it in. I dont know what to do. I called HP and my warranty expired 17 days ago. 17!!!! They didnt do much and basically told me it was because I didnt use it when I first got it. I turned it on the day it came and then put it back in the box until last October when I bought a desk for it and started using it. Thats why I dont know why its not working. Because It hasnt been used that much. Its basically as good as new.
Computer Name: HP TouchSmart 23 AiO PC
Model No. 23-d040t