Starter neutral switch is not fun...

hi from uk the switch you mention is called the inhibitor switch which prevents cars engine from being started if in gear but allows starts only if in either neutral or park mode question? do you hear click on key start position? or just nothing? may i suggest you check the starter solenoid which is on starter and has positive cable from starter attached along with a thinner cable? also you will/should see a thin wire also connected to the solenoid on a seperate teminal this is the wire from key start ign switch and when key turned to start energises the starter into operation /turn engine ensure this wire is clean/secure? one other thing to check is the earth/ground lead that runs from chassis/body and connects to engine usually in vicinity of rear of engine? all above is assuming that your battery is ok?? hope this helps?