I never played the game and it has been a very long time since I saw the anime but as I recall there was no mention or hint that any of the guys in Nayuki's school ever tried asking her out. I would figure a girl like Nayuki would have a bunch of guys gunning for her.

I guess this is because it is a harem story and the MC is the only male of consequence.

I remember there was that little joke in Lucky Star when Konata wondered why no one ever tried asking out Tsukasa since she seemed like she would be very popular with the guys. Then she figured they were all terrified of Kagami.