lots of possibilities:
1. LCD is bad. your phone IS on but you can't see it because the display is black. try the vibrator button. if the phone vibrates, then you most likely have a bad LCD.
2. loose connection inside phone. check all connections to LCD and battery
3. main logic board went kaput. in that case, the phone is toast.
4. charging port doesn't work any more. battery is drained and the phone cannot get juice through bad charging port. this can be replaced very inexpensively
5. probably more but I would start with these top 4.