I just had a quick look at an old case of mine that also has an LED display.

My Turbo switch actually has two sets of 3 wires coming out of the back of the switch (one orange, one black and one white).
One set runs directly to the turbo switch header on the motherboard, whereas the other one goes directly to the LED display.
The wires running from the turbo switch to the LED is purely to change the reading on the LED, when you push the turbo button in or out (based on the jumper settings that is selected - or the DIP switches in your case).
At the back of the LED display, there is also a set of wires (one red & one black) that is connected to the 5V side of one of the molex plugs (which makes sense, in order for you to able to supply power to the LED display). However, this was only present on older PSU's and later ones didn't even have this separate wire.
The reason for the 3 wires on my turbo switch is due to the fact that different motherboards had different layouts in terms of their headers. Case designers then sometimes had connectors that actually had the "+" wires connected to the middle and outer pin so that you could connect the connector to either a two or three pin header.

It appears your LED display is "integrated" with the rest of the switches in the front your case (the Turbo, Reset & Keylock switches) as well as the Power, HDD & Turbo LED's. This would explain the whole "mesh" of wires coming out of the back of your LED display's PCB board.

As for the wires coming out of the LED display:
I noticed a loose black wire in your second picture. Where does this wire run to/from?
You will notice that the one brown wire goes into the "+" side of the connector, whereas the other one to the "-" side of the connector. I would just connect one connector to one pin on the motherboard and the other one to the other pin (you can just twist each connector to the "outside" to make it fit).

I do find it a bit strange that your Turbo LED connector only has a red wire (which normally donates the "+" side). There should be a black wire for the "-" side.
Try and find the connection point for the Turbo LED indicator and see if there isn't perhaps a loose black wire (take note that the Turbo LED indicator is usually "driven" by a signal from the motherboard, not from the switch).
However, you can normally safely connect these any way you wish to the relevant headers on the motherboards. If you connect them the wrong way around, then your turbo LED will come on when it is in "de-turbo" mode. You can then just swop it around. The same principle applies to the Turbo switch.

As for the DIP switch settings. Once you get the wires connected, you will just have to play around with the DIP switches until you figure our the "pattern" or configuration.

Thanks for such a detailed reply, that wasa great read.

The loose black wire that you see is the same black wire from the TURBO Swith, I had to cut all the wires from the back of the TURBO switch (the black one and the 2 brown ones) in order to be able to remove the front plastic cover of the case, hat is why it seems loose but in fact is cut, I will solder these back to the TURBO switch once I out the case back together.

The 2 brown TURBO +- cables have both the brown wire connected to the '+' in the pin header, there are really identical cables (seem like duplicates). The fact that both are babies connect to the '+' is not clear in the picture because the brown cable on the right is slightly angled.

I am wondering if we could match the cable color order and functions of 3 wires coming out of your TURBO swith (TURBO button) that connect to the TURBO switch on the motherboard, with the cookout order of mine,
If We were to map these out; What would be the color and function equivalent in yours?
In mine from top to bottom:
BROWN -
BRONW -
BLACK -

I will also post a picture of the case itself in case that someone has a clue on why the cablin fin this case seems so unusual.

Added Pictures of the Case.
Anyone knows about this brand 'PC II 486"?

Big red power switch, LED display, some would consider that the ultimate case!