If I'm understanding you correctly you turn the car on and all the lights come on
you turn the key and nothing happens -
Try a few more times and the starter kicks in and the car starts.
so it sounds like the starter is not kicking in so the next 2 places to look are
1. The starter motor relay - in with the battery could be sticking
2. the starter solenoid - on top of the starter - could be sticking
If it was me I would dive under the car with a multi meter (or a 12v bulb) and pull the small wire off the starter motor (there are only 2 wires to it battery feed and solenoid feed)
Stick the meter/bulb into the wire and ground the other side, get someone to turn the key to the start position several times, if the meter shows 12v (or the bulb comes on) every time then the solenoid is sticking or U/S if it is an intermittent feed then it's the relay.
If you want to test the starter motor best to take it out of the car ,
Run a 12v feed from a battery to the starter motor big cable earth the starter motor to the same battery run a extension from the small wire on the solenoid to the same battery when you touch this wire to the live terminal the bendix should kick out and the starter motor spin - make sure the starter is secure in a vice or similar they kick a bit when fired off the car!!!
Hope that helps
EDIT : I'm assuming you changed the clutch switch for a known working one so that is ruled out.