The next logical step to take is to see if you have a feed to the exciter/fire wire to the solenoid when the key is turned to the start position,this can be done with a multimeter or test light.If you have a feed,then your looking at a faulty starter or possibly a corroded earth connection between the engine and the battery/body.
If you don't have a feed,then you need to check the back of the ignition switch and see if you have one there.If not,then the ignition switch is faulty,if there is,then there is a problem with the wire between the starter and the switch.As far as I know there is no fuse in that wire,so if it is suspect then it must be damaged or corroded internally.
There is also a possibility of by-passing the feed from the ignition switch to the starter to check the operation of the starter,but I'm not sure if I advise anyone to try it unless they know what they are doing to be honest.You can 'jump' between the battery feed to the starter and the solenoid exciter/fire wire connection,but you have to be very careful doing it.
As said before,neither the immobiliser or the
sensor will prevent the engine from turning over,it has to be a problem on the actual starter circuit or an earthing problem on the engine.