You say the cables were connected, and ask whether to re-connect. To what?
In your new photos the very wide connector at lower centre is a SATA power connector. Is this one normally plugged into a SATA power output connector from the PSU? If so, it then provides power to something -a circuits board or whatever - that has other ports on it to plug in some things. Right?
Most lighted fans now have TWO cables coming from them - one for the motor, and another for the lights in the frame. On your rear fan the LIGHTING cable I expect is the one that has the two connectors on the left. OR, maybe those two are on a cable that goes to a central circuit board so its signals can be distributed to the rear fan AND the front panel lights.
The two connectors on the left prompt a thought. SOME fans have a cabling system to allow a daisy-chain connection. That is, for several units (say, fan motors) to connect to a single mobo header (or other source), you plug in a FEMALE connector to the source, and then the MALE connector coming from that same fan is used for plugging in the SECOND fan's female connector, etc. Thus you get a chain of fans connected from one to the next, and only the first fan is connected to the source. Now, to do this on one fan you COULD have two separate motor cables coming from the fan with male and female connectors (such a fan with lights would then have three cables), OR you could have a single cable with TWO ends on it, one male and one female. I suspect that is what the two on the left of your photo are. OR maybe these two are for the LIGHTS in the fan frame, set up for a daisy-chain connection. I NOTE that those two are NOT the "standard" connectors used for fans today, they are unique to the fans with your case. That is why I suspect there is a central circuit board where they plug in, and that board gets power via a SATA source from the PSU.
That leaves the male connector with 4 pins at upper centre. What is that? It is not any "standard" connector for fan motor or lights. Is it the cable to the front panel lights? Where was it plugged in before? A circuit board, or the female connector on the left?