Some of the answers above have a few errors. But to be complete about the advice, we need to know exactly what mobo you have - maker and exact model number. With that we can check the capabilities of the mobo CHA_FAN headers. So please post that info back here.
While waiting for that I can offer some things for sure. First, the way to connect the H100i system - do what its manual says. It has one cable from the pump unit that must be plugged into a SATA power output from the PSU to provide power. Then there's another connector (3-pin female fan type) that plugs into the mobo CPU_FAN header. The manual notes that this connection serves only to send the speed signal from the H100i system to the mobo header for monitoring, and that's why it should go to the CPU_FAN header and not to another. It is NOT involved in control of cooling. Then the two fans that are on the radiator unit must plug into two sockets on the end of a cable from the pump unit, and NOT into mobo fan headers. Then you need to connect a cable from the pump unit to a USB2 header on your mobo. Finally (and this is not clear in the manual) you are supposed to download from the Corsair website their free utility Corsair Link and install it. The Corsair Link software takes over control of CPU cooling, using the temperature sensor inside the CPU chip and its own settings (adjustable by you in Corsair Link if needed) to communicate to the pump via that USB cable and control the pump and both radiator fans.
Now, on to the case ventilation fans. The case comes with three 3-pin fans, and the ONLY way to control the speed of such fans is to use Voltage Control Mode (aka DC Mode), so you cannot control them directly using a mobo header that only can use PWM Mode for control. However, the case also comes with a unique device, the Phanteks PWM Hub. Used correctly, this unit provides a good solution. You MUST plug the cable from the Hub that ends in a 4-pin female fan connector into a mobo CHA_FAN header that is configured to use PWM Mode - it MUST have a PWM signal to operate. Then you also MUST connect a cable from the Hub to a SATA power output connector from the PSU to give it power. Since you seem not to be able to get fans on your Hub to work, I suspect this connection may not have been made. Finally, you plug all your case ventilation fans into that Hub, ensuring that one of them is on the Hub's white Port #1. This is the only Hub port that can send its fan's speed signal back to the mobo for display and checking. If you don't plug a fan into that port, your mobo may start sending out error warnings about a failed case fan.
The Phanteks Hub uses the PWM signal from a mobo header to create internally its own group of six 3-pin fan headers that use Voltage Control Mode. That mode is NECESSARY for controlling 3-pin fans, and it CAN control 4-pin fans, too. You do not have to restrict yourself to 3-pin fans when using this Hub. However, you don't have any such fans for case ventilation, so don't worry about that. Using this Hub is how you can control 3-pin fans using a 4-pin header operating in PWM Mode.
The "problem" in all of this use of the Hub is that it only can do its job if it gets a PWM signal from the mobo CHA_FAN header, AND it has a power supply from the PSU. For the power supply issue, check that you have made that connection. For the PWM signal issue, we need you to post your mobo details so we can advise how to ensure it will work.