[trebor]

For now forget the relay wiring as the GSM should come on when you power up the unit with a series of LED flashes including the handshake with the sim card, just checking that the power you have is permanent 12v and not switched and that you have the sim card in as not clear on the picture ? ( there is a protruding bit but is that printed on the board or the actual sim ? )

If above good double check your supply and earth and dont dismiss that the unit could be faulty as Lewis has had some problems along the way.

By the way to save a bit of space you can jump the 12v and common on the board save having 2 wires in for both.