There has been a spontaneous resolution to my problem with accessing the BDP-3.
I’d not used the unit in over a month. When I turned it on a while back, I had the problem described in my initial post. After a week or so with no luck on getting things to work, I posted my issue here.
Today, in preparation for a call I was going to make to Bryston support to work through the problem, I turned on the BDP-3 and went in my browser to my.bryston.com.
Everything worked.
Aside from having put the unit into service mode three days ago, I hadn’t done anything else to try to resolve my problem. I turned the player off after it had been in service mode for a few hours, and not until today had I turned it on again.
I don’t know what's happened, but I’m glad my player is working again. I’m still curious about what might have led to the problem I had. I hope it doesn’t return. I’ll ring Bryston straight away if it does.