pay for the repair yourself then file in small claims. have somebody look at the screen to see if the logic board repair stressed the screen at all. you want to implicate that the repair was the cause of the cracked screen because there is no other damage. the burden in small claims is very low; chances are that filing the action will get you what you want.
if you didn't break it, why should you pay.
if you didn't break it, why should you pay.