my laptop is a HP and is 8 years old
8 years is good going for a laptop. Chances are it's going to cost you the thick end of a new one to repair.
Assuming that you've tried it with and without mains power and it doesn't boot either way, then here's the most likely reasons for it's demise:
Battery is dead - Some laptops can be booted up on mains only, so if you're not getting power to the laptop from mains then unplug it, remove the battery and connect it to mains again. If it boots then the battery is kaput.
Hard drive is dead - if the laptops power light comes on when it's connected to mains, but the hard drive doesn't spin up, then the hard drive is probably shot. It can be difficult to tell whether it's the cooling fan or the hard drive that's vibrating - a fan will make a consistent noise/vibration, whereas the spin vibration from a hard drive varies (especially at the very start of bootup). A suspect hard drive will cut off very suddenly almost immediately that it starts to spin up - sometimes all you hear is a clicking sound.
Dead screen - Some older laptops won't boot if they can't display anything to the screen. There are two things that could cause this - graphics chipset is buggered, or the screen is shot. The best way to test this is to plug in a monitor (assuming that you or someone you know has one handy). If nothing displays then the chipset may be shot. This would mean a new motherboard.
Motherboard is dead - if the laptop power light doesn't come on when it's connected to mains then the motherboard could be shot.
Memory has become dislodged - bit of a rare one, but it's possible that one or more memory sticks has become dislodged from it's clip. They are usually found on the underside of the laptop and behind a small cover held in place by a couple of screws (some laptops don't have this cover though and you would have to take it apart). The memory sticks slide into long thin sockets and are clipped in at either end by springy bits of metal that fit into small grooves. If you're even contemplating doing this yourself then make sure that you have the laptop plugged into the mains AND the wall socket switch is defintely switched OFF (this acts as an earth so that you don't accidently zap the memory sticks with static).
Apart from the battery, the rest are going to be pricey to fix if you take it to a shop . i.e. 50% and upwards of the price of a new mid-range laptop.
As Pow-lo said earlier - wherever you go, steer clear of PC World. I wouldn't trust them to sit the right way on a bog seat.