Most of those pictures aren't in focus, so it's hard for me to tell what's going on, but I can see that you have way too much bare wire exposed on almost all those wires. You should only have enough bare wire expexposed to cover the solder pad / joint, no more. Having all that extra exposed wire could lead to shorts, which it almost looks like it happening right now. I would recommend desoldering all those wires, trimming back the exposed leads, and resoldering them before doing any kind of power testing to minimize the chance of shorting. Once that's done, we can tackle the issue of the fan not spinning if that's still going on.
Update: I rewired the connections from the usb-c pcb to the rvl pms board, ensuring that less bare wire is exposed. When using a multimeter the expected voltage was entering the rvl pms board from the batteries, but it does not leave the board (the usb-c pms and the fan are not receiving any power). Is this an issue with the rvl pms or is there something I can do to troubleshoot further?
I'll second dababy, please post pictures of what the wiring looks like now (and please make sure they are in focus!).
Let's go through this together. For right now, it might be best to bring this all down to the bare bones, and test from there. Disconnect everything between the USB-C PD Board and the PMS, with the exception of BTN and GND. Disconnect the fan for now as well. All that should be wired up to the PMS for bare functionality are B+, B-, BTN and GND.
From there, measure your battery voltage. If the batteries are below a certain threshold voltage (I believe it to be somewhere around 3.5 volts, but I'm not 100% positive), the PMS will either not turn on, or otherwise not function correctly. If your battery voltage looks good, press and hold the button on the USB-C PD board for 2 seconds. Measure for voltages on each of the voltage pads on the PMS. If everything looks good there, you can add the wires to the USB-C PD board back in.
Basically you just want to start with the bare bones, and slowly add each piece, testing between adding new parts.