As flecc says, the battery appears to have taken a charge and is stable under no load conditions.
Does it have condition monitor leds on the battery and if it does are they all illuminated when the battery is turned on by the switch and the test button pressed?
Under load conditions the internal battery wiring, key switch, fuse and output connector, followed by the mating half of the output connector to the main controller supply wires must be in sound condition to deliver power to the controller, the next step on the route.
You now have to test the battery under load and for that you need to have the control system fired up in sequence.
If any part of the sequence fails it needs to be fixed before going onto the next part of the sequence.
The main controller consists of two main parts:
The power delivery circuit and the user input circuit which controls the power delivery circuit.
From reading your operating manual I think these are the following steps for sucessful operation:
1. Turn on the key switch - provides the battery supply to the main controller
2. Press the throttle (red button) on/off switch - the throttle battery level lights are illuminated showing the main controller now has power on it and gives an indication of real voltage level of the battery.
3. Press hi/lo illuminated buttons to select level of assistance - the main controller requires one of these must be selected before allowing outputs from the pedalec sensor or throttle to become active.
4. Select boost button (green button) on/off (if fitted to your model) - adjusts maximum power delivery level requires one to be selected before allowing outputs from the pedalec sensor or throttle to become active (if fitted).
You now have two options:
5a. Twist throttle to give motor power - outputs a variable voltage level to the main controller to switch power to the motor.
5b. Turn crank to activate pedelec sensor and or overide the pedelec sensor by twisting the throttle - upon turning delivers output pulse signals to the main controller to switch power to the motor .
Ofcourse the motor and its wiring also needs to be of sound condition for the bike to work.
From what you have already said it looks like the problem is the hi/lo switch unit is not operating correctly hence my suggestion to swap it out or borrow an identical one or check the connections between the box and the main controller first.