you have the hi current BMS with all the extra mosfets.
are any of the leds lit at all? the gate voltage on the mosfet has to go to about 5.86V (on mine) for normal operation.
if you look at the pcb you can see the opto isolator chains running down the side of the BMS. the outside row is the opto chain for the HVC signal that turns off the charging mosfets (the two in the corner) when the voltage on any cell climbs above 3.90V.
if you look you can see a trace running down from the outer corner of the last opto to the source leg of the charging mosfet.
both mosfets are connected in parallel. you can test the mosfets to see if they are damaged.
if none of the leds are lit then none of the cells is high enuff voltage to have turned off those mosfets, so they should still be turned on and the gate to source voltage would be that 5.86V.
so there are two avenues. 1: the mosfets are damaged and are open circuit so the current will not flow through them. 2: one of the opto isolators is turned on because of something happening to it or has shorted those two outside legs of the opto on one of the channels.
you have some electronics training as i recall so you know that the mosfet has what is called a body diode between the heavily doped silicon that makes up the drain part of the semiconductor, and the more lightly doped source region. you can test the mosfet by measuring the source drain diode to see if it conducts in one direction but not the other. this tells you if the silicon inside has been damaged by large current flowing through the body diode.
to test the body diode you have to disconnect the BMS sense wires. that removes the source of current from the battery that drives the BMS circuitry. you don't wanna be measuring with the diode tester when there is voltage on the diode.
when the sense wire cable is unplugged, (you can unplug at the black plug if you wanna since it is easier to reach, or at the white plug where it plugs into the BMS pcb) you can measure the diode between source and drain.
set the voltmeter to the diode tester position. to test the diode, you put the red, positive, lead on the source leg (anode of the body diode) and the black probe on the drain (cathode). the reading will be in millivolts and that is called the forward bias of the diode. it will be the same for both of the mosfets because as you can see they are wired in parallel so the voltages will always be identical. same is true for the gate voltages, and also for all of those output mosfets. they are all the same because they are all connected in parallel. as you can see by looking at the traces.
when you reverse the voltmeter probes, putting the black probe on the source leg, and the red probe on the drain leg, then the diode tester will read open circuit because the diode doesn't allow the current to flow backwards.
if the mosfets do not show a forward bias and are open circuit in both directions then that is where the problem is.
if not there, then we can test each of the opto isolators to see which of them is turned on.
here is the opto data sheet: http://www.fairchildsemi.com/ds/FO/FOD817A.pdf
if you look at how the 817 opto transistor works, you see where there is a small dot in the corner of the 817. that is next to the anode of the gallium arsenide led that turns on the transistor part on the outside of the opto. the current is delivered to the anode of the opto from the voltage comparator, the 6 pin IC, tied between the hi and low of each channel. you can follow how the trace runs from the comparator to the anode. you will see a current limiting surface mount resistor in the trace to prevent the opto from taking too much current.
if you look at how the traces work on the underside, you can see that there are two traces running down from the top to the bottom, and each trace is attached to either the collector of the opto transistor (the top leg) or the emitter (bottom leg). when the opto transistor is turned on, then that shorts the two traces together so the voltage across the two drops to 0V. by looking at the traces and how they run down to the charging mosfets, you can see that if the two traces are shorted, then that shorts the gate to the source and turns off the mosfet.
you measured .5V across the gate/source and not 0V. i think this is significant but it is not clear if that is because the gate of the mosfet itself is shorted which we can learn from your diode testing so do that first. you can use the diode tester on the gate to see if it is shorted internally to either the source or the drain. there is a 1 megohm resistor usually between the gate and source but it should not show up as a short in your diode test. it would be below the resolution of your meter, 1^-6 volts.
hope that helps, lemme know what you find and we can go further to examine the optos too, if that is the problem.