If you can connect to Telstra and Optus hotspots then this implies that the Samsung TV can communicate using WiFi and you have correctly configured the TV with the correct WiFi parameters. Assuming that the Netcomm device has been used successfully to connect to the internet then that means that the Netcomm device is also able to communicate using WiFi and that TPG is therefore not at fault (as far as internet access is concerned).
What you need to do is to check once again that the Netcomm device is using the same frequency band as the TV. The modem I have has two bands, 2.4GHz and 5GHz, each of which can be enabled independantly of the other. I would recommend that you ensure that the Netcomm device is configured to whatever WiFi parameters are used for the Telstra/Optus hotspots and give it another try.
Also possible it's using a technology or technology variant that the TV doesn't support. When in the process of setting it up it could be 'dumbing down' the connection temporarily until he applies it (I've seen this before).
You could try changing the security settings or wifi 'technology'.
E.g. change security from WPA2 to WPA, change Wireless N or AC to Wireless G/N/AC. G is older than N, which is older than AC
I tend to run wireless in two segments. 2.4ghz runs ONLY B/G, 5ghz runs ONLY N/AC - mainly because then I can tell exactly what can see what (the two segments are somewhat separated enough that older devices will more often only see the 2.4ghz, and newer can see both)
Thank you for the update.
Given that your modem and TV is about 10 meters away from each other with one thin partition wall in between. Have you tried moving the modem right beside the TV just to check if it can detect/connect to the signal that the modem is broadcasting?
The connection from the phone/DSL wall socket is not needed as we only need to check if they can communicate with each other.
If the TV was able to detect the WiFi connection from the modem when it's near or right beside it, then the distance or the strength of the signal is the problem. But if the TV still can't detect the WiFi connection of your modem, then that's really a mystery.
If you are going to purchase a new modem, then we will suggest that you purchase a modem that can support the NBN technology in the future. We've checked your address and the technology will be available in your address from January - June 2020.
We don't have any brand that can suggest, but hopefully our community will provide some inputs.