Your power switch is 12V rated. The black and orange leads that are bent back and disconnected (2nd pic) are the LED leads from your switch. I suspect that they are intended for the LED pads on the Sigma 22, which are right in front of the green terminal block in the middle of the two long black terminal blocks. However, there's something going on in that position shown in the first photo. It looks like there's some electrical tape or some sort of black plastic covering the LED pads in front of that green terminal block.
After cleaning up whatever that black plastic is - if you are VERY careful, you might try pushing those leads into the LED holes on the PCB. (Do this with the power OFF.) Then try turning the power on. If the switch lights, note which wire is in which hole and solder them in place. If the switch doesn't light, turn the power OFF, then switch the wires and try again. If the polarity is reversed on the LED, I doubt seriously you are going to burn the LED out - as long as you don't leave it on too long.
Anyway, just a suggestion. If you had it repaired from a reputable service person, it really needs to be returned to finish the work, because they left things hanging.
P.S. Not being that familiar with the Sigma 22, I'm a bit surprised there's no polarity shown on the LED pads. I can't find any looking at AMB's website on the Sigma 22. The polarity is shown in his schematic, but not on his drawings/pics of the board. At any rate, you might "assume" that the orange lead for the LED is positive and the black lead is negative. Looking at the schematic, the positive lead (orange) should go next to R16 and the negative (black?) next to R17.