Am I interpreting your question correctly?
You have what you describe as a BTET2110 BT Freeview box.
The box will not turn on or off via the BTET2110 remote
You can change channels OK via the BTET2110 remote.
You cannot "get sound" from the box via the BTET2110 remote.
Don't understand your comment about "retuning the remote".
Suggest you check the TV sound settings (with the TVs remote)
Suggest you check the HDMI connectors are fully home.
I cannot find any reference to a "BTET2110" TV box by anyone and certainly not BT or Humax (or Humex).
Please check model numbers and repost with a clearer description.