I suspect that it is the connector.
Greetings. I have mostly B&G on my boat, which was 'upgraded' from Raymarine before I bought the boat. I have only one of these T41 displays on board. I'm disheartened to hear that B&G service is poor or non-existent! With Raymarine you didn't always get the answer you wanted, but at least they were responsive and repairs are available, albeit at prices that often made buying a new item more attractive.
I wonder, why do you think it's the connector? If it just failed spontaneously, I can't imagine how it could be the connector, but I'd like to learn!
Have you sought an independent repair person? Do they still exist? I worked in a marine electronics shop while in college in the 80's, fixing just about anything electronic for boats, including sailing instruments. We had all the service manuals, etc. (I wish I had all of those vintage service manuals!)
It's a shame, it could be something simple inside. Components
do go bad with age. I wonder if service manuals are available from Navico.