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Are you using the same or an updated router for the NBN connection?
Previously worked with a Telstra Partner however I am not a Telstra Employee, just a fellow customer helping when I can.
LD there could be any number of things effecting your Chromecast, but NBN as such wouldn't be one of them.
Chromnecast depends on a 2.4 ghz WiFi connection. As long as you've got your regular internet connection and a reliable WiFi hookup to that for the Chromecast you shouldn't be getting any problems.
There is an excellent trouble shooter you could check out and follow at this link: http://www.whistleout.com.au/Broadband/Guides/Chromecast-not-working-with-WiFi-help
I shifted our Chromecast today from one TV to another and struck problems. Did a complete reset of the chromecast and bingo, up and running again.