First, the transmitter only works if it is pressurized.
Second, confirm that Transmitter 1 is set to the correct ID. It should match the numbers on the transmitter.
Third(ly?), while the transmitter is pressurized, go to dive mode, then do the battery check, it should check the vt3's battery first, then the transmitter's battery.
Lastly, the transmitter only works within a certain range of the vt3. The manual will say exactly how far and in what area, but for testing purposes, just put your vt3 on top of the transmitter.
If none of that works, I'm lost, but I think it's probably dead, send it back!