BBB powers from USB but not from 5VDC, cape powers only with 5VDC

I gather the BBB can be powered either by USB or by 5VDC, but not both.

So I don’t understand. My BBB does not power up at all with 5VDC connected. As soon as I connect USB, however, it boots right up.

Meanwhile, I have a cape (CBB-Relay) that requires 5VDC. It doesn’t work unless I then connect both USB and 5VDC.

As I’ve read more than once, it can be powered either by USB or by 5VDC.

But what am I supposed to do when I need to power it by 5VDC to get the cape working, /and/ I want to be able to use the USB connection for development?

If I’ve fried my BBB while trying to figure this out, why would it work at all with both 5VDC and USB connected (realizing that it can be powered either by USB or by 5VDC, but not both)? It works just fine, and in fact the only way it works, is if I connect both 5VDC and USB.

What am I missing?

Sounds like the board has been damaged and needs to be repaired.

Gerald