Strange behaviour

I have -91 legend L 2nd gen. Been a fine car thus far but recently it has had problems with starting (cranks but won't start, engine check light stays on) but always after several time opening/closing driver's door with key it usually starts nicely like nothing's wrong.

Could this be because of bad actuator in the door (I know this car has alarm system but does it have an immobilizer also?) or maybe ignition switch? I have changed main relay and done all the usual checking mentioned with this forums threads and everything seems fine.

This is getting frustrating so please help!