You don't need a PIC programmer to do this, but it can be used to write to an EEPROM - however, you are rather assuming that the EEPROM is causing your fault?.
There's no relationship between a 24LC64 and the PIC16F876 though, so I've no idea why you mentioned both?.
Why not just buy a new blank EEPROM, plug it in, and see what happens - often if you fit a blank EEPROM the TV will detect this, and write the factory default values to it.
Is the TV a Samsung?, these are well known for capacitor problems, and causing damage to the EEPROM.