Not a waste of time.
Although it is possible, it is unlikely the BT module is faulty. You don’t say what module you have. Is it a HC-05 or a HC-06 (Bluetooth Classic)? It is important to determine exactly what module you have.
Different modules have different firmware. This means different command formats and (in some cases) different baud rates.
Getting no response from AT commands is normally a problem with the connections, or the baud rate, or the format of the commands. Assuming you do have a HC-06 try upper case commands, lower case commands, then the same again using different baud rates. 38400 is also common.
If you still have issues look through the other website. I have information about various BT modules there.