The best way to start out is by doing the below listed procedure for Emergency start procedure if code has been lost.
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The '80s and '90s BMW models (E23, E24, E28, E30, E32, E34) that have the separate On Board Computer units (OBC), such as your E30 chassis (3 series 84-91), have an anti-theft feature available within the OBC. If this feature is activated, the pre-set 4-digit code must be input. When activated, the starter will turn, but the engine will not start. After 3-attempts, the horn will sound for 30-seconds.
It's likely that accidentally activated the anti-theft by pushing the OBC CODE button while the key was in the #1 position (perhaps listening to the radio). They may have just been lucky enough to push the buttons in the sequence that ended up storing a code and activating the system.
The owner's manual for your 325ic gives the sequence and instruction for activating, using and de-activating the system, but there is no mention of what to do in case you "forget" the code you input. However, the owner's manual for a later model E34 chassis (5 series 89-96) does mention an emergency procedure for the system. So, give it a try. If this does not work try just disconnection the battery for 15-minutes, or so.
EMERGENCY START PROCEDURE - IF CODE HAS BEEN LOST:
* Disconnect battery for 5 minutes, or more.
* Reconnect battery.
* Turn ignition key to position 1 (alarm should sound).
* A time display will appear and run down to zero (for 15 minutes).
* After 15 minutes, the engine can be started.
During the waiting period of 15 minutes, the code can be re-entered.
* Press CODE button.
* Input desired code.
* Press the S/R button.
* Start the engine.