|On some laptops a fully expired battery can stop the laptop powering up on mains power so try removing the battery.|
Also, you will definitely need a new battery if you do manage to get the laptop working again on mains power. If a battery is left uncharged for 3 months or more it becomes unusable and won't charge up.
If the laptop will not power up even with battery removed then it's obviously something more serious and you'll need to let a laptop repair centre take a look at it if you think it's worth spending money on it. But be prepared for them telling you "sorry we can't help you if it won't power up". That's what I got told when I took a "dead" laptop into my local repair shop for a friend.