I have a theory on what is happening and why we seem to be getting a different story from each end.
There was an initial outage that was put down to “a fault with the device that manages the interaction between our network and all of the different types of customer modems” according to a statement from a Telstra representative.
UPDATE : 22/5/2016 12:35
It looks like some subscribers are having success by performing a factory reset on the gateway/modem/router and then re-entering the account details.
At this point in time it is not a fix recommended by Telstra. My recommendation is to replace the router/modem if it is more than 12 months old otherwise, refer the fault to Telstra.
*SPECULATION AHEAD* I could be way off on this.
I have seen a few Telstra clients and it seems initially that the fault may have also impacted customer routers DHCP servers and either corrupted or simply disabled the DHCP server.
The role of the DHCP server is to pass out network addresses for all client equipment on at the clients premises and without a network address computers, tablets, phones and media devices are unable to find a way out to the internet via the router.
Because the router is connecting to the Telstra network and authenticating, Telstra sees a connected router which is usually associated with a successful connection but the client is unable to have their equipment connect to the router meaning from their point of view the internet service is still down.
This is a theory but I expect to be looking into this further to confirm if this is the case.
In the meantime, try to find an alternative solution for situations like this or go chat to your family and friends. Chances are they might need comforting too if they are struggling with web-withdrawal.
If you are at least semi-savvy with your router and you are having problems, you could try connecting via a static IP assigned to a computer and accessing the router (usually 10.0.0.138) to see if the DHCP router has been disabled or if you have a spare router try connecting that up to see if the problem goes away.