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...
1. Unplug your charger cord.
2. Remove the battery.
3. Press and hold the "Power" button for 30 seconds.
4. Now plug back in the power/charger cord.
5. 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: If it will turn on when the charger isn't attached but not when it is attached, then the likely problem is the charger. When they go bad they often will not be able to both run the device and charge the battery at the same time.