Hi,
- Try with another battery
- Try with another charger (not with the laptop USB)
- Clean the battery connectors on the phone
- Try to charge the battery externally
If you phone switch-on normally with other battery but again have a problem with the charging, then you have a hardware problem. This can be broken USB connector, charging line on the mother board or charging i.c.
If you phone can't switch-on, try to enter in the Android Recovery menu and reset it, or try to flash it with Odin. But if you phone can't enter in the recovery mode (Home + Volume Up + Power) or Download mode (Volume Down + Power) you have a hardware problem with the mother board. For this operation you must use a fully charged battery.
Regards.