You're diagram looks pretty good, but with one significant mistake. You connect the anode of all LEDs together, and then put all resistors in parallel, connecting to the + supply. Give me a bit, and I'll draw up the "proper" schematic for you.
Just about a week ago I made an NXT program to test cables. It requires one NXT, and one physically-free motor.
When you're running it, it will instantly (within a few ms) start beeping if wires 3, 4, 5, or 6 get dis-connected. If wires 1 or 2 get disconnected, the motor will immediately begin to float, and once it slows down, the NXT will detect it and start beeping (could take a second or so).
It does not determine which conductor is shorting.
I'm all for gun control... that's why I use both hands when shooting