The CZ-1, for example, when plugged into a power supply that doesn't fully deliver the required current, can "seem" to be powered on, with LEDs lit up and everything, but may not respond properly or make strange or no sounds.
What are the power requirements of the AZ-1 and what are the specifications of the power supply you are using?
Even if these two things match, are you sure the power supply (if old) is still operating to spec? Can you try another power supply?
Also, does the AZ-1 power up and operate properly when powered by fresh batteries?