Yes, that is very odd…unlucky pins and all.
You are doing those continuity tests with the power off, correct? Are you sure your meter’s battery is good and it’s working correctly?
Are you referring to the “power led” or the “bypass led”… when you said it is connected to pin 13 of the microcontroller?
With the opamp…that is very unusual that pin 13 isn’t connected to the board somehow. With the power off, do you get continuity between pin 13’s pad and pin 13 on the IC? If not, try soldering the pin to the top of the baord. Do you get continuity between the pad of pin 13 and the pad of pin 14?
Lets try some higher order logic…When you test the relay connections as per the troubleshooting guide (5-C), does it appear that the relay is working as it should? (do this test with the power on so you can switch the relay).
Let me know what you find.
-Brach