My HP nx7300 will not power up. The LED doesn't even come on when I plug it into the AC supply

You could have a faulty power adapter or the power input socket on the laptop is faulty. Check the power adapter plug that plugs into the laptop with a multi-meter. The voltage reading should be slightly higher that the voltage that is printes on the label on the bottom of the adapter. If you get a zero or low voltage reading then the adapter is faulty and needs to be replaced. If the adapter is OK then the power socket on the laptop is faulty, it may only need to be soldered due to a dry solder joint or replaced if faulty. To check if it is a loose connection, wriggle the plug in the socket and observer the charge LED, if it flickers on and off, then the power socket may oly needs resoldering. This requires the laptop to be dismantled to get access to the power socket.