If the above is correct, here is how I would proceed.
Power ON. HALT and RESET.
Set all of the switches SA0 through SA15 to OPEN. The data bus LEDs should all be ON.
Power off and remove IC U12 - observing the correct polarity of the IC within the socket for subsequent installation.
I am 'hoping' that this will cause the LAD signal to float HIGH (due to the action of the weak pull-up resistors on the inputs of the connected 7405 gates).
Power ON. HALT and RESET.
Test signals HAD, C3 and NOOP again (with your logic probe). I am hoping these three signals should all be LOW. If not, report and stop.
In theory - with the 7405 inputs HIGH (due to the signal LAD being pulled HIGH due to the internal pull-up resistors) the outputs from these 7405 gates connected to LAD should all be LOW.
By CLOSING switch SA0 - this should cause the data bus LED D0 to extinguish. The other data bus LEDs should remain illuminated.
By OPENING switch SA0 - data bus LED D0 should illuminate once again.
Repeat this test for SA1 through SA7 in turn (CLOSE followed by OPEN) and data bus LEDs D1 through D7 (respectively) should extinguish and illuminate.
If this is the case, power OFF and re-install IC U12 in the correct orientation (as found). Check for any bent pins on IC U12 after installation.
Report the results.
Dave