01 1.5 Would not start immediately - tyrian

I tried to start my 2001 Kia Rio this morning

1. Upon turning my key the first time, the car turned over very very slowly but did not start. All the lights on my dashboard, radio, electric windows worked
2. Turning the key the second time produced nothing at all - the car did not turn over. All the lights on my dashboard, raio, electric windows still worked as usual
3. Left the car alone for two or three minutes
4. Tried started the car again for a third time - it worked perfectly. Car started immediately.
5. Drove to work and parked my car (it was urgent)
6. Two hours later when it was time to go home, the car started immediately.

Possibly relevent information: I had a new alternator fitted last month.

Can anyone tell what the problem I had this morning was? A faulty ignition switch?

Thank you