zerothread?id=140879
second last post in above thread shows location of inhibitor relay for auto transmission cars. its is in relay box next to battery. you might find the same relay to do substitution.
the original starter was clicking and humming which obviously means it is getting power which suggests weak battery or dead starter. you should have tried hitting starter as that wakes them up if they are bad. bad starters are intermittent.
i guess you could have a weak connection in the ground or 12v+ circuits.
supply 12v positive directly to small wire at starter. that will tell you if the complex positive circuit is working ie inhibitor relay, inhibitor switch, wiring, ignition switch, etc