I have had this same problem for several years on and off !!!!!!
Sometimes it would take ages for the car to start but I didn't want to take an intermittent problem to a garage that they could not see. I did all sorts of silly things to try and get it to work, rub the key, take it out and put it back in, spit on it, push the car forward or backward a couple of feet etc
Eventually I discovered that taking the key out and turning the steering wheel into lock and then unlocking it sorts the problem every time.
I don't know if there is any logic to this?