If the laptop is quite new, then there shouldn't be anything wrong with any of the parts. So it is going to depend on what you mean by 'new'.
Additionally, if 'new' then it should be under warranty. Which means changing anything or opening it up yourself would void said warranty. If that is the case, it is the manufacturer you should contact.
Now if it isn't in fact new, then you can try the following...
NOTE: Yes, I know some batteries are not so easy to get to, on some devices. However, it should be removable/replaceable. Unless it is under warranty, then you should contact the manufacturer first.
Try the following and see if it will turn on...
- Unplug your charger cord.
- Remove the battery.
- Press and hold the "Power" button for 30 seconds.
- Now plug back in the power/charger cord.
- Now put the battery back in.
If this doesn't help, then test the power cord to see if it is good. Either try your cord in another device, or try another devices cord in your laptop. You may also want to try charging it when the device is off, rather than on. If it works then, the cord is probably the issue.
Should that not be the problem, then check the battery to see if it needs replacing.
If you do not feel comfortable doing this yourself, then I would try a local tech.