Why won't my HP Pavilion g series turn on?

The description is too vague to fully understand the issue, but just from what you said I’d assume one of these have happened:

A)Battery possibly may have died and needs to be replaced. B)AC:DC power converter may have burned out (power brick). C)Mobo/CPU/etc may have broken from overheating.

Option C is the worse scenario so try the first two (cheapest solutions first) and see what happens.

I’m thinking your charger either isn’t making a good connection or is broken. See if a friend has a charger that will match your laptop, or try taking it to someplace like Best Buy or Radio Shack and see if they have a universal charger you can try.

If it doesn’t work with a different charger something is mostly likely broken inside. You could try a new battery, but if they light doesn’t come on with a different charge I’m guess the charge port is broken.

The ac adapter or the AC jack in the back of the laptop, where the laptop adapter plugs into, could have become separated from the motherboard inside. That happens quite a bit. Try another power adapter and if it doensn’t work then it could be the ac jack or your motherboard could be fried. In that case it may not be worth fixing. But you can remove your hard drive as all your data it’s still there.