No external display output - even after replacing logic board...

I'm stumped on this one. I had a machine which intermittently failed to send output to an external monitor. I tried different adaptors and monitors on it. Eventually it was just out entirely and wouldn't display a signal.

So I replaced the logic board. To my amazement, the problem persisted. I tried SMC and PRAM resets but there was no change. I ran an ASD and it didn't show any issues over multiple test loops.

When I connect an external display, the internal display blinks out and back, as it normally would when detecting an external monitor and sending a signal to it. But it never gets a signal. System Preferences - Displays doesn't show that a display is connected.

Oh wise iFixians, do you have any idea what this could be?