Hi Robert,
Here are some initial troubleshooting ideas, you may have already tried these:
Does pressing the power button (the button closest to the Ethernet socket) make any difference to the voltage at pins 7,8, even briefly?
It may be worth testing with no boards or other devices attached, just in case.
Finally, although you're seeing 5V from the PSU, it could be worth trying a different one (or trying to power the BBB from the USB connector via your PC) just in case there's some strange issue with the 5V supply collapsing under load.