This is likely an issue with the battery. Please first check to see if the battery is properly put into the laptop, and try turning on the device again. If the battery is put in properly and the device is still not turning on, you may have to replace the battery. The battery may not be holding charge which will not allow the laptop to turn on.
To replace the battery, please go to the following page: [[Samsung NP305E5A-A03US Troubleshooting#Section_Device_Will_Not_Power_On]]