Wtf? Why not get change the plan or something. I am with telstra and I have BigPond Elite Liberty* (100GB) - ADSL $79.95 monthly and get up to 20000/1000kbps.
To the main issue.....
Put in your browser http://10.0.0.138/ << Default IP for telstra modems.
What you do is log in with details "Username: default" and "Password: default" once that happens that allows access to the speedstream settings "Blah blah blah" unless you have changed that... (Hope not)
You should see your IP address or PPP setup with IP address in "Green" meaning your on the net, I suggest look at this while connecting to a page and then see if it goes "Red" meaning "Disconnected"
If that happens you should be able to read the Logs of the modem down the bottom somewhere (I Forgot because I have a new Thompson router and modem) and what it has done on the side bar, it may lead you to what is happening. Personally when I did have the SpeedStream 4200 series I had same issues my problem was relating to the Reset Button on the back of the modem being stuck. Resulting in unknown resets.r