I have to ask, what was going on with it just before the problem started? Dropped, updated, etc?
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.
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.
It could be a few things. If it is under warranty, I would really suggest you contact the manufacturer and have it repaired. If it isn't, then it will depend on how comfortable you feel with doing the work yourself. However, if you don't have good testing equipment, and it isn't under warranty, then I would suggest a local tech.