There's an explanation of the BMS connections in a photo in this link:
https://bmsbattery.com/bmspcm/714-10s-13s-20a-lithium-bms-for-bottle-battery-09-bms-pcm.html
The cell pack positive (B+) goes directly to the output terminal. Both the charger (C-) and output (P-) negatives are interrupted by the B.MS. The BMS opens the connection between the B- and P- when the switch is on and all the cells (B1 to B10) are in the range 3.0 v to 4.2v).
The LED in the switch must conduct the current for the switch. If it doesn't come on, either the switch doesn't switch on or there is no power on the positive pin of the connector.
Things to check:
Voltage between battery positive terminal (B+) and B-, which is pack voltage.
Connection of the B- and P- to the BMS.
Connection between P- and output terminal.
Individual cell voltages - black probe on B- and red probe on each B1 to B10.
Voltage between B- and each of the two pins on the switch connector.
One of the above results will indicate what is wrong. Try and stick to a logical approach rather than trying random things.