If you have tried multiple cables, it sounds, unfortunately, that it might be the Lumia 900's connector.
If you can shine a bright light into the connector (my eyesight would require me to use a magnifying glass now) just to check that there are no foreign objects like pocket lint; that might find something. While I had not had this happen to my Lumia 900, it had happened several years ago with my iPhone.
Otherwise, the connector might be loose from the main board, especially if the phone had ever taken a tumble while it was plugged in. Hopefully, it would be the former and not the latter.