Does the on/off switch disconnect the battery? If not, where do the wires connect to the circuit board? It'd be funny if it was something simple like the switch.
As those fets attached to the aluminum fins in the upper left of photo 728 are close to the big red wire (assuming battery +) they're probably the power out of the battery controlled by the BMS, so I'd check those fets first. If you have the battery hooked up, rather than do as the video recommends, I'd test the voltage at the gate to negative and the drain to negative.
If the gate doesn't have voltage, it'll most likely be something in the on/off switch or a BMS sensor that failed (e.g., low voltage cutoff stuck in the off position). If the source and gate both have voltage and the drain doesn't, then bad FETs.
You can probably "jumper" past to test the rest of the system by shorting the source to the drain (just be gentle and don't pull a lot of amps ... essentially you want to see if any of the display lights up).
Update: Before inserting probes into a live device you should probably yell "SMOKE TEST" or "Here, hold my beer" (it's tradition after all).