Picture is fine, but I don't recognize that model. But since it doesn't come on, it indicates a power issue.
Next step is to measure voltage at the battery connector like you say. When measuring here, it can sometimes give you a false reading if there is nothing connected other than the meter. But see what it gives you and also measure the voltage across the charger jack if possible. If the BMS is working and not tripped, the voltage on the charge port should be exactly the same as the discharge wires.
Is that the dual motor Apocalypse scooter?
"One test is worth a thousand opinions"