Some things to check :
- does the usb port have some visible damage? (broken or bend pins)
- test the charger with something else to see if it might be the charger itself.
- use an USB cable and just connect the switch to a PC. Leave it for an hour to charger.
In the beginning it will be charging very slow.
- remove the SD card and try turning it on.
- if you have a modchip installed, maybe the LED of the modchip will give some indication.
All the colors have some meaning.
- you can open it up and check if the battery still holds some charge.
if that is the case, then the charger chip might be broken.
But I would recommend leaving that to a repair shop.