majenko:
That looks right, and the fact that touching wire 2 turns it on (probably flickering at 50/60Hz) means it's wired fine. It sounds like the output you are connecting it to though isn't actually running as an output, and the connection is floating.
Ok, but how could that be? If I take the transistor out and just have the LED connected like: 5V - resistor - LED - shift register pin - it all works just fine. I can I get it to work properly?