Can you carefully measure A2 and A7? It may be easier to just measure the center wire on each level of the volume control, as they connect to these pins.
Something sure isn't adding up, a glowing LED means 1.57V on the cathode, you have a nice amount of voltage at T1/T5, and there aren't enough parts in the kit to be replacing the 22K resistors with something else (they'd have to be higher, and there aren't two higher value parts in the kit).
Essentially, this means that the voltages at pins A2/7 can't be correct, which would indicate an issue with the grounding on the volume pot, or with the connections of the wires leaving the pot and going to those pins on the 9 pin socket.