You will not damage the motherboard inserting it the wrong way.
Same applies for LEDs - you won't damage the motherboard and you won't damage the LEDs because the voltage and current "sent" to the leds is too low.
You can figure the polarity with a multimeter ... put the meter in voltage mode, connect to the two wires and gently press with the eraser tip of a crayon on the piezo element inside.
If the wires are connected to the multimeter correctly (positive to red probe , negative on black) you would see a very brief voltage rise on the multimeter. If it's wrong way you'd see negative voltage on multimeter.