Try a direct connection to the modem.
UrbanGrunt came up with a step by step guide.
Step 1: Remove the homehub from the modem
Step2: Connect your pc/laptop into the modem using LAN1 port (LAN2 is disabled and not in use)
Step3: Open network and sharing centre on windows and click set up a new connection or network
Step4: Connect to the internet (the top option) then click make a new connection Broadband PPPoE
Step5: Username Internet@btbroadband.com and the password as broadband
Step6: connect, for some reason it may say that it cannot connect, just keep pressing try again if this happens and it will eventually connect.
If you can connect OK then the HH4 is at fault, if not the problem is either with your modem or between you and the cab.