This is a very strange story.
Why would they change the spark plugs an cables? Doesn't make sense.
I had a problem with my micra that it flooded (is that how you say it in English?)
What I did was remove the airbox cover so the engine got more are and then with some trouble it started.
But if it's still the clicking noise (and the startengine doesn't go around nicely) it's definitely the battery or the connection to the battery.
Can't you film it maybe?