I think you are saying the modem is sync'ed to the exchange, which I asked a while back.
If I'm right, try this. Is there a Reset button on the HH? Should be accessed with the end of a paperclip into a small hole, probably at the back. If so, while the router is on, do that gently but firmly, and hold it pressed until other lights start flashing. Release the button and wait while it restarts. See if you can then connect.
If that fails, somewhere in these forums, (sorry off-hand I don't know), there are the BT login details you need to connect by linking a computer by ethernet direct to LAN1 on the modem, ignoring the HH. (I assume the Home Hub is connected to LAN1?). You would then have a connection.
But it does sound a bit like your broadband account at BT Retail hasn't been activated
My broadband basic info/help site - www.robertos.me.uk
My domains,website and mail hosting - Tsohost
. Internet connection -
Plusnet Value Fibre.
"Where talent is a dwarf, self-esteem is a giant."
- Jean-Antoine Petit-Senn.