RDP Display is Black and Connection is Brief

We have a laptop using a desktop monitor / display (VGA).
It's been working fine for a long time.
Suddenly we couldn't RDP into it.  The problem appeared to be the trust relationship with the DC.  
So, that's been fixed and we no longer get the message "your Windows Domain Controller cannot be contacted for NLA"

However, NOW RDP connects and displays a black screen.
And, it appears, the connection terminates within a minute or so.

I've tried all manner of things with the display settings, etc. to no avail.
I've tried to update the display driver on the client.
This is happening with more that one initiating computer on the same client/target.  Other clients seem to be OK
I only see one display to manage - I don't think that's normal.