I'm no immobilizer expert but looking through the service manual code 51 is an immobilizer fault 'code cannot be transmitted between the key and immobilizer unit'.

The troubleshooting guide starts with:

1.checking the main, ignition & backup fuses,
2.checking the battery (min 12.8v open circuit),
3.check the main switch for continuity
4.check the immobilizer system wiring

And then checking for various voltages on the immobilizer itself. (I'd recommend getting a service manual!)

I'm sure someone with more knowledge will chime in with more info, but at least you can make a start with that!