There may be a reset button, which acts like plugging the battery in some devices. Look for a pinhole. If you can't find the direct one (as there can be many holes on a laptop) then I would suggest you search for the devices manual or layout of the laptop online to help you locate the pinhole. Once found (if it has one) use something small, but not sharp (don't want to do any damage) to depress it. See if this will help.
You may also want to check and make sure your charger cord is actually OK and charging the laptop, as well as make sure the battery is actually charging. Either of those can make it not turn on.