My computer won't turn on.

[hellllppppmeee]

So I bought an HP touchsmart 600-1120 (bkb9aa) a little over a year ago, and used it infrequently for about two months before I had the internet disconnected because I lost my job. Over the past year it has been sitting on my desk and used to play a game once a month, if that. When I came home yesterday from a weekend away I was calling to get the internet connected again and realized the computer wasn't on and it didn't turn on. I removed the plug from the surge protector and tried an outlet on another wall. It didn't turn on. I tried to reset it by disconnecting the power and holding in the power button then plugging it back in. It still didn't turn on. Today I spent an hour on the phone with a lady I could hardly understand and had me on hold for an hour and fifteen minutes out of my hour and a half call. She had me do the same thing I did yesterday then started talking jibberish about multiple cords and wouldn't comprehend that there is only ONE cord and that's the power supply. The block on the power supply has a green light that comes on when I plug it in but the computer does not turn on. Can anyone help me? Or should I hire a translator to.speak to HP for me?