The button on the battery you press to show the state of charge: Hold it down for several seconds... it may wake the battery BMS up (it does on my TranzX CAN-bus system - I don't know your A2B so it may or may not).
Most smart BMS battery boards go into low power (sleep) mode when not used for a set period of time to reduce consumption... the 8v you measured at the output suggests that. Once the BMS in the battery wakes (if you can force it to), it should give you the full 41v you measured inside but at the output too.
If that doesn't work, I would be checking cable continuity between the display and the battery; if the bike fell with no visible signs of damage, but the display doesn't work at all, the owner may have grabbed/pulled on the cable(s) to save the fall. My logic here is that pressing the on switch on the handlebar should send a pulse to the battery to awake the battery, yet you say the display is dead.
EDIT: I just googled and found your A2B model has a removable display; contacts on removable displays are always dodgy - give them a good clean. One other final thought: Bosch CAN-bus systems have a battery in the display for memory/function which causes problems when old/flat; possible A2B do too. The bike is an old model; that battery may need replacing. Otherwise, I'm out of ideas and would try contacting A2B to see who has one of their plug-in diagnostics systems.