99 bmw e36 323is coupe wont start

when you say sensor i assume you mean switch, right? does it have a conventional single/double throw, single pole switch to enable the starter? how did you wire the relay? the clicking indicates a back feeding current that is half-triggering the relay. it's probably wired wrong or the coil needs to be diode isolated. this can fry a relay and/or blow a fuse. check all the fuses under the hood and inside (they're in the glove box behind a panel i believe) make sure they are all ok.

The OEM security system should NOT prevent the starter from cranking.  It will prevent the motor from turning over or cause it to die quickly if it does happen to start.

I would investigate the clutch interlock to make sure it is working as designed - your problem is most likely there.

There should be a wire on that switch that goes to ground when the clutch is depressed all the way.  Set an ohm meter to the diode test function.  This is a picture of the symbol of a diode.

Touch and hold the black lead of the meter to the chassis of the vehicle, or any other ground.   Then touch the red meter lead to the wire coming off of the clutch switch.  Press the clutch pedal to the floor, if the meter beeps constantly, your switch is working.   If there are multiple wires on the switch, you will need to test each wire.

you should be able to check the switch by metering each wire individually and determining whether any of the three wires change polarity when you 1)press the switch in and 2) press the switch in with the ignition turned to the start position.

please be careful when you do this! for obvious reasons. you dont want the car moving while your lying halfway out of it. put it in neutral and put the parking brake on.

oh and remove any wiring you've integrated into the clutch switch circuit first. if it has three wires, one should be a reference voltage; another, a starter circuit enable; and finally, maybe a cruise control disable.