(Hint, right click -> open image in new tab to make it much bigger)
With everything unplugged (other than the CM3 in the CS board) using a multimeter in continuity mode (so that it beeps when the probes touch), the pins with the same letters/colours should be connected (and therefore beep). So A->A, B->B etc..
F* is the only one that doesn't have a resistor to test, to test this one you need to remove the CM3 and in the top corner pins, it's the 5th one from the top (running the probe past these pins should make it beep). The screenshot is the top corner of the CM3 slot.
You may find that you need to wiggle your probe on the resistors slightly because they're kind of covered in a film/oxidisation so a little scratching with the probe will loosen it to test.
Please let me know how you get on!
So far I've gone through two boards, two cm3's and 4 sd cards. These boards have to work, there's no explanation as to why they won't boot. But to dismiss user error which it still very well might be I'm sending everything back to you. Here's pic's of my simple build. The pics are in order of build process. I connect the screen ribbon, place the board in the shell, connect the hdmi/usb and power switch, place the cm3 in the board, connect the battery and insert the sd card. I flip the switch and I get absolutely nothing.