Nice VERY pink bike, kit is exactly the same as mine. I think they are not common as they aren't the cheapest by any stretch, but they last don't they?
Being not common is probably why you can't find a charger to borrow.
At the end of the day, if this charger can't be got going, then an alternative can be sourced, once pin polarity has been checked.
On another note, I see your motor cable exits the axle directly upwards. It would be best if you found a bit of slack to form a drip loop, so the cable exits the motor downwards then turns up. Helps to keep rain and condensation out of the precious motor.
You obviously have excellent taste. This one has lasted since 2012 albeit with a replacement LED display and controller. Thanks for the tip, but it isn't going out in the rain, in fact right now it isn't going anywhere..
The relay still clicks, as usual, but normally that precedes the yellow light and the fan, which aren't following now.
This morning I wired the charger up to an incandescent bulb to simulate a load. It lit the bulb dimly, and entered a repeating cycle of relay click, bulb on, relay click, bulb off, but at no point did it turn on the yellow light or the fan.
Presumably the issue could still be either the charger or the BMS, and another charger is probably the best way of working out which.