Power: it is +5VDC.
- Check what model transistor those are at the very top of the board in the picture. See if they're PNP or NPN.
---If PNP, put a multimeter on the emitter and test for a short between it and one of the header pins. That will be your (+) lead for 5VDC. The collector pin of the transistor will go to the ground pin.
---If NPN, put a multimeter on the collector and test for a short between it and one of the header pins. That will be your (+) lead for 5VDC. The emitter pin of the transistor will go to the ground pin.
- Ground pin should be right next to the +5VDC pin at the header on the very top of the picture. If I had to guess, +5VDC/GND is 2 of those 3 pins you don't have hooked up.
To connect power outside the case, you can use a 9V battery jumpered to a breadboard. Then run the battery output on the breadboard to a LM7805 to output 5VDC. Alternatively, you could snip a USB cable and wire up the 5V/GND to it, powering the circuit from an old phone charger. It would be best to wire up a 2-position female header so you don't short something on accident.
The single brown (orange?) wire likely goes to the motherboard turbo LED (-) to get the signal for the turbo display to change state when you press the turbo button on the case -- the turbo switch is probably hooked up to the motherboard turbo switch header.
To get your speed to display right, one set of headers (left/right in your picture) is for the 1's position, and the other is for the 10's position. Each segment on the display is A-G. There are 4 positions for each segment -- always off is jumper removed. Always on is one position. On for turbo enabled is another position. On for turbo disabled is another position. From your picture, look as if each segment is 4 pins -- you have one base pin, and 3 surrounding pins. Jumpering from the base to one of the 3 adjacent pins gives you the latter 3 positions I talked about. In the picture, the right hand jumper row (probably the 1's digit) looks to be jumpered to display always zero (0) -- segments A-F, omitting G with no jumper to keep that middle segment always off in both turbo/nonturbo states.
You'll have to experiment with it, because I haven't seen this particular model turbo display and I'm not 100% sure on the documentation because none of my diagrams 100% match up with it.
