Okay, let's start with the basics, is there a light bulb on the A/C Adapter?
If there is, then when it is plugged into a wall outlet, is there any light shining thru it?
If not, get another adapter.
Try pushing the power button from the right corner, or the left corner... I've had a few issues with the power button on hp systems, it seemed to do the trick...
If it still doesn't turn on, try unplugging the battery, then turn it on. If the battery is already unplugged, then try plugging it in and tuning it off with and without the A/C Adapter connected.
If that doesn't work, then tell us, and then, if your willing too, we can help you get into the laptop to see if the power jack, or the "power button" is broken.... Or, your system might be fried, or just plain dead.