As several have said, the LIGHTS are completely separate from the PUMP electrically, so all that has no relationship with OP's problem. The INTENT of this AIO system from the perspective of the PUMP and RAD FANS is this: The PUMP's 3-pin female connector should go to the CPU_FAN header OR to the AIO_PUMP header. That provides power to the pump and sends the pump's speed signal to that header for monitoring for failure. The RAD FANS should be connected (using the Splitter supplied) to the CPU_OPT header IF you plug the pump into the CPU_FAN header; OR put pump on AIO_PUMP and FANS on CPU_FAN. This will provide power to the fans and have their speed controlled automatically by the CPU temperature sensor.
Now, some points to check.
1. In either scheme for connecting above, it is important that the BOTH headers be set to use the newer PWM Mode - see the BIOS Manual, p. 10, at upper right in the drop-down selector. (Not the User Manual.) Do NOT set for Voltage or Automatic. For the rad fans, this is the correct type of control. For the PUMP, this uses a quirk of 3-pin fan and pump design the guarantees the pump's power supply from Pin #2 is always the full 12 VDC for full speed operation as designed.
2. OP says "Yes I put thermal paste". BUT also says the AIO Pump unit arrived with a plastic shield over its bottom contact surface, presumaby to protect a thin layer of pre-installed thermal paste. This means that the sytem now has TOO MUCH thermal paste in the gap betweeen CPU chip cover and pump bottom. A thick layer of paste there actually is BAD because it slows the rate of heat removal badly. IF that is the case, then OP needs to do two things: FIRST find out the RIGHT way to apply that thermal paste he has - look up how much to use for YOUR particular CPU chip type, and how to place the pump unit on top, spread the paste and tighten the pump down properly. THEN you must remove the pump, clean off all the paste you have on there, and re-do as instructions say.
3. Whether the pump it plugged into the CPU_FAN header or the AIO_PUMP header, that header normally monitors the SPEED signal sent back to it from the pump for NO signal - that is interpreted as a failure of CPU cooling. If that happens it pops up a warning message on your screen for a short time and then will shut down your system fairly quickly without even waiting for the temp sensor inside the CPU chip to show high temps. This is to prevent damage to the CPU from NO heat removal. Thereafter it also may refuse to allow you to start up if there is NO speed signal on that header right away as you try to boot. So IF your pump actually has failed and is not running, this will prevent any start-up attempt.
You can try a test for total pump failure this way. This is a TEMPORARY set-up to defeat that protective process, so do this only briefly. Disconnect the PUMP 3-pin lead from whatever header (CPU_FAN or AIO_PUMP) you have been using. Plug into that header instead the lead from any known-good fan so the header WILL get a valid speed signal. Now plug the PUMP into a CHA_FAN header. Boot into BIOS Setup immediately and go to that CHA_FAN header and check what it tells you for the"Fan Speed". This is really the{PUMP speed. If it is working it may show you a fast speed like 2000 RPM or higher, or some lower speed in the hundreds. BUT if it shows NO speed you know the pump is NOT running. Do this quickly, then shut the system down before the CPU gets too hot. Change everything back to the normal connections. Now you know whether the pump can work at all, or not.
4. When an AIO pump is operating properly is is very quiet and smooth. So it can be very hard to detect that operation by feeling for vibration or sound. A better technique IF you can get it to work at all is to feel for the TEMPERATURE of the hoses when the system is running normally. At the PUMP end, one hose should feel warmer than the other - not hot, just different. Same at the rad end - one warmer than the other. If there is NO temperature difference at both sites, then there is no fluid flow and the pump has failed. IF both hoses at the PUMP end are equally warm and the hoses at the rad end are both cool, same fault.