Lets start with the power, make sure it is charging by looking at the ring on the side that lights up when the power cable is plugged in. If this is on, then make sure the light on the front of the laptop is on. If it is charging and it is detecing power(2 lights will be lit) then you are okay with power. If the lights are not turning on, then it might be your charger. This is rare, but its worth a try. Get your hands on another identical one. Make sure the Watts line up or else you might blow something out. If it is not your charger, then it is probably an internal part such as the power plug or the motherboard. In either case, unless you really know what you are doing, then you would simply need to replace these. Before you order a new one online, keep reading.
[skip this part if your power is not working]
Pull out one stick of RAM, then try to start up. If this doesnt work, then try the other stick(put the first one back in). If that doesnt work, then try the hard drive. If this doesnt work, then try the wireless card an any other attachable devices(that connect directly to the motherboard). If this does not work, then the problem is in your motherboard and you will probably need to replace it.
[If your power is not working and/or it looks like you need a new motherboard, read this]
Be sure to contact HP first, they are doing a recall or as they call it a "service enhancement" to some of their malfunctioning laptops that are having motherboard issues. You might want to research what the service enhancement covers first. This will be important when dealing with the representative. Also make sure you try a lot of things with fixing it, even if it seems rediculous such as cleaning out the fan. The more it looks like you tried to fix it, the more likely they are to service your laptop under the 'service enhancement'.
Here is more info on the service enhancement. Be sure to read as much of it as possible. Sometimes the representative on the phone will try to say it isnt covered beucase it doesnt match the symptoms exactly. Try to show them as much as possible that it does fall under one of the defects listed and they will most likely fix it. This is a one time shot though, be sure you dont screw it up!