Welcome to the forums! Interesting problem. Have you tried replacing the battery in the key fob? (clicker). Is the immobiliser factory fitted or is it aftermarket? Have a look under the dash for a little button or toggle switch. If you find one, put your key in the ignition and turn it to the 'ON' position, then within 5-seconds press and hold the button until the little flashing LED in your dash goes solid (it should chirp once too if you have a siren installed). This
should override the system and allow you to actually start the car. If you manage to get it started I'd recommend taking it to an auto electrician and getting the problem diagnosed. Best of luck