Pyzar not starting every time


I have a 1997 Dyhatsu Pyzar ('Move'?). It starts every time after having being left garaged overnight. But, if I try to re-start after having driven it for a while, it won't start. It can take from 10 to 40 turns of the key before it does eventually start.

After each turn of the key there is a soft hummmm sound that seems to run down the centre of the car. I can always tell when the next turn of the key will start the car because the hummmmm turns into a hummm-thwang sound. (Can you tell by now that I'm a mechanically-illiterate female ...??)

Mechanic No.1 fitted a new ignition switch. The car went OK for 2 days but then the problem returned.
Mechanic No.2 thought it was something to do with the thermostat (?) so he replaced it ... the car went OK for half an hour, then I parked it for 10 minutes, the problem returned.

Mechanic No.3 has replaced the spark plugs, removed checked and cleaned the air filter; checked and cleaned the throttle body, distributor cap and rotor contacts. He checked the battery (battery is less then 12 months old)and it's OK. The car started perfectly first time, when I left his garage, but next day the problem occurred again.

His computer shows that the electricals are OK, but funny thing is, I turn off the radio while I'm trying to start the car and after a few turns of the key the radio comes on again. This happens often.

I have tried starting the car with my foot flat to the floor on the accelerator, but that doesn't work either.

Mechanic No.3 really wants to fix this problem for me, so he and I would be extremely grateful for any advice please.