Thanks very much everyone. I'm sure you're right - that the cells are faulty. The considerable inrush current must load the weak cells such that one or more parallel groups exhibits a low voltage which is enough to trip the BMS, so the display can't power the trike up. Had it been my battery, I would have opened it long ago and probed around. But it isn't, and I don't want to return a tampered-with battery to my friend because I wouldn't be able to guarantee its safety. What I've done is I've fitted the inrush limiter and it's working OK - enough to enable the trike to operate with assist, so I can return it at least. I'll discuss the options with the owner.The BMS cutting off power when the pack was at 36volts is a pretty good giveaway that one cell group is much lower than the other cell groups. The pack seems to be unbalanced. Sturmey's suggestion of opening the pack and checking the voltage of all of the cell groups is a good one.
My guess is that you have one parallel group of cells that has lost capacity ( or possibly very much out of balance). Its coming up ok on charge but it discharges early and this low voltage of one cell group will cause the BMS to do its job and disconnect the load.
I don't get it. If you leave the battery connected to the controller, there is no inrush when you switch on because the capacitors are on the unwatched dive of the controller.
Thanks again!