First, you need check whether the battery was charged or not. You can charge the note for 1 or 2 hours using the official charge. Then try to reboot. If not, remove the battery, and try again.
Normally, you should NOT use notebook or PC to charge your tablet because the current from USB port (500mA) is too low for the battery.
Anyway, if you are sure the battery is charged, but you cannot start it, you can always ask for a replacement.