Is it the horn or alarm siren?
If its the horn then disconnect both horns located under the front of the car either side, you will have to remove the under tray panel to find them. If its the alarm siren that can be coded out, its under one of the rear wing liners.
Whichever it is sounds like the wiring is shorted out somewhere as soon as ignition is turned on, matter of checking the wiring and maybe the horn push at the steering wheel.
Take a look at the Electrical Wiring Manual here for the circuits
An Electrical Troubleshooting Manual Specifically for 2000 Z3 and Z3M cars in Great Britain. It includes the interior movement sensor used in the DWA security system.
zroadster.org