GPS works fine on Arduino Uno, but doesn't work on MEGA 2560

Development Tools IDE 1.x
2

Take these out, Serial.begin() takes over the pins:

int rxPin = 0; // RX PIN
int txPin = 1; // TX TX

pinMode(rxPin, INPUT);
pinMode(txPin, OUTPUT);

You are using a breakout cable or something to connect the Rx/Tx port to both the GPS and the PC?