I know things take time with BT but being without any connection at all and raising the ticket last Friday I would have hoped something would have been done by now. (yes it has been logged with BT but there is a 48-72 delay before they even think of doing anything, at least that is my assumption seeing as how nothing has been added to the ticket). I have answered the magic questions that were posed (although some did cause amusement - like have you tested on another line or have you tested with other equipment - who has these spare!).
What that will mean is that the remote testing was unable to identify a fault or couldn't tell if the equipment was properly set up and connected. You'll likely have been called to check this before we reported the fault onto BT.
Regarding trying an alternate modem or line, we know that this isn't possible in every occassion, but it can help in the diagnosis of the cause if you have a friend or neighbour whose modem you can borrow for 5 minutes just to rule in/out your hardware as the cause.