Problems syncing Gmail contacts to iPad mini.

I just bought and iPad mini (first Apple purchase) and I have tried everything to sync my Gmail contacts with it. I tried the Microsoft Exchange feature and even adding it via CardDAV, but after it is complete and I go check my contacts app, there is nothing there.

Any tips on how to make this work?

Is there a way to sync them using iTunes on PC? I am also having troubles installing iTunes, I will go leave a message about that in the appropriate section.