From the sounds of it, I think something has gone wrong on your module to brick the firmware as it should be showing up as a bluetooth device.when its powered up.
However here are a few more things to check. Can you run the
AT+VERSION command and see what you get back. Also sometimes depending on what bluetooth module you have, you might need to add \r\n at the end of each command, so typing AT would be
AT\r\n, and to change baud rate you can try
Otherwise if none of that works it might just be that your bluetooth module is bricked