So it appears you have found the reason for not booting is a PSU issue. But I'll explain why the connector is 3-pin, etc. and how to ensure it is set properly.
Control of the speed of older 3-pin fans and newer 4-pin fans is done differently. IF you have a 3-pin fan and plug that into a 4-pin fan header that IS using the new PWM Mode of speed control, that fan will always run full speed - no control. Now, the PUMP of your AIO system is SUPPOSED to run full speed all the time. So it is wired just like a 3-pin older fan and you DO plug it into the CPU_FAN header. But this is IMPORTANT. Many mobo CPU_FAN headers now are designed to be able to do either type of control, AND they have an option in configuration of that header in BIOS Setup to allow Auto configuration. When set that way, at every start-up the mobo tests what is plugged in there by trying to change its "fan" speed using the PWM signal system. If it cannot, then it switches to the older Voltage Control Mode so that it CAN control its "fan" speed. BUT that is exactly what you do NOT want for the PUMP! So you need to go into BIOS Setup for the CPU_FAN header and make sure it is NOT set to "Auto" - instead set it to PWM Mode. That way the PUMP plugged in there will always run full speed.
There's another factor here. A very important second function of any fan header is to monitor the SPEED signal coming back to it from its "fan". NO speed signal is understood to be a fan FAILURE and you get a warning. But many mobos do much more than that for the CPU_FAN header. They may completely shut down the system if they get no fan speed signal at that header to prevent damaging over heating of the CPU, and they don't even wait for the temperature sensor to indicate high temps. This also means that they will not let you start up with no speed signal at that header. So something must be plugged in there. Now, of the several components of an AIO system, the most critical to monitor for failure is the PUMP - if it fails, you get no CPU cooling very quickly. If one or both rad fans fail, the temperature rises on the CPU chip will be much slower and other protection systems will work for that. So you must plug your PUMP into the CPU_FAN header to allow it to monitor the pump speed.