vfr and I have differing procedures of checking for battery fault finding.
If battery is open I always start with cell group voltages first and write them down as a list 1 -10 readings for 36v lion to rule out a cell fault first. Then I work backwards from here, if they work out ok and are ok I carry out wire continuation and pack voltage readings from and to the BMS via pack charge/discharge and from discharge and charge ports to BMS not forgetting any switch if fitted as these can malfunction.
Sometimes a bad/dry solder joint can be the issue.
Zero volts on the charge socket means that there's an interruption between it and the cell pack. I already said that if the BMS was switched off, there would still be some voltage on the charge socket, so no point in checking the cells. Logic and testing tells you where and what to check, not just go round randomly checking whatever comes to mind, starting with the most difficult things.
For no charging, simple steps to discover the problem:
1 Measure the charger voltage and the charge socket.
2. If either has zero volts, that's the one to investigate. Goto 5. and 6.
3. If you have any volts on the charge socket with a value below the voltage output terminals, the BMS is switched off so open the battery and check the cells to find out why.
4. If the two voltages are the same, but low (say less than 33V for a 36v battery), one or more cells have dropped below 2.5v, so open the battery and charge those cells.
5 Zero volts on the charger - check the fuse and the connector.
6 Zero volts on the charge socket - check the charge fuse (if it has one), open the battery and check where the interruption is.