Go to the options and turn off the TV output setting

Replace the LED. Desolder the old, most likely burnt out,LED the replace it with a new one.

Google the part. Then replace it your self if you dont want to send it to apple. btw why do you still have a 2nd gen

Well its ether one of two(maybe both) 1. you port is bad, depending on how long you have had the psp the port can get worn out. try blowing on it or buying a new port then replacing it. 2. The battery is bad. the battery can be shorted out. ether replace it with a known working battery or buy another From experience I say its the battery but for my brother it was the port.