I have a 120V to 12V adapter with a molex end that I want to use to power a PC fan controller. However, the pins on the female molex (the 12V adapter) doesn't have holes that fit with the pins from the male molex (the PC fan controller molex connector). This figure shows the problem I'm having. Is this normal? From my understanding of molex connectors, the 12V adapter molex connector 12V ground pin is missing, and for the PC fan controller molex, the 5V ground pin is missing. Also, when connected like that, the molex connection would be in a 7V configuration. If I'm correct, the fan controller needs 12V + 5V to function correctly (which my 120V to 12V adapter is supposed to provide). So why both connectors pins are not correctly aligned?
Both manufacturers have assumed that whatever will be plugged into the other end of their connector will have both ground pins fitted & connected together (usually a safe assumption).
They therefore assume that they can save 1 or 2c on each unit by only fitting 1 ground pin.
Unfortunately for you, they each picked a different pin to fit.
If you have any access to the back of one of the connectors, you may be able to gently tease the ground pin out of the hole its presently in (you may need to depress/bend some little tabs on the side of the pin) and fit it back into the other hole such that it now lines up with its mate in the other connector.
The ground pin is not connected... One solution would be to move the ground pin on the fan controller cable to the proper position. If you look at the pins closely, you can see 2 small tabs bent out from the pin itself that keep the pin in place. With a small screwdriver, you can gently bend them back to be level with the pin itself, and pull out the pin gently with the wire attached.
Now you have to bend the tabs so that when you put the pin back in, it will keep the pin in place. (Be sure to double check which hole you put it in...)
In normal cases, this should not have posed a problem, as the power connector should have both ground sockets populated and connected together.
For why the panel does not work
The hackish 7V wiring you included is irrelevant in this case. The panel most likely does not work that way...
That trick would use the voltage difference between the 5V and 12V rail to get 7V. However, as you can see from the pictures that means actually connecting the negative supply lead of the load ("black wire" in this case) to +5V, and the positive supply lead to +12V.
Your panel has 3 wires going to it: the GND, +5V and +12V. Most likely it is designed to have all of them (or at least GND and one of the positive supply rails). It can not just "find out" what you plugged into it and adapt to what it has, you have to have it connected properly - but without a schematic, or at least a board picture it is very hard to guess...