Should the buzzer go on whenever key is turned? It seems a stupid question, but the lights dim and solenoid clicks uselessly as well. I'm checking grounds etc...
Is the buzzer sound like a "beep beep beep" or a steady buzzing? If it's the former, it's most likely your low-air-pressure warning which won't go away until you get the engine running and the compressor compressing; if it's the steady buzzing, you probably have an emergency window or hatch open (or you cut the wires to them).