Dennis, the brake switches do actually close the circuit when either of the brakes are used, but unfortunately this does not cut off the 5V supply, so it would not cause your missing 5V feed.
Either the 5V supply is being somehow shorted to ground, or the regulator chip on the controller that provides the 5V output has failed.
With the battery disconnected, check the resistance between the +5V and Ground wire to see if there is a dead short.
To give you some idea of what you should expect, I measured a resistance of around 2,900 Ohms between the +5v and ground connections on my controller's 8 pin socket.
The 5V supply for the throttle also feeds the three hall sensors on the motor, so the motor cannot run without it.
If your resistance reading is similar to mine
(indicating that the 5V circuit is not shorted out) I would try applying an external voltage
(i.e. three AA batteries in series) across the red and black wires on the pedelec connector to see if the motor would then run. If this cures the problem, it should theoretically be possible to use a cheap external DC to DC converter to replace the failed internal regulator and supply the required 5V feed.
But are all three lights on the throttle supposed to be on? I really expected to see only the full light.
When the battery is fully charged, all three LEDs should be on. As the battery voltage starts to fall, the LEDs will start to turn off in turn.
Three LEDs = Full
Two LEDs = Half Used
One LED = Almost Empty
Unfortunately these gauges do not seem to be too accurate, and you may find that the battery shuts off much sooner than you might expect.
It's a bit like the battery level indicator on my phone, it seems to stay on full for ages and then it suddenly decides to go from reading full to being flat enough to shut everything off in a very short time.
Alan 
