Hi, got my new S4 approx a month ago, got it out my pocket last night and noticed only the AMOLED screen is cracked, spoke to Samsung customer service just now, who wasn't very helpful and they basically they said it was physical damage, this was in a Aegis case protector and had a screen protector fitted too, so basically told them it seems the phone is not fit for purpose, to which they told me to go see the phone provider I bought it off!!! Any thoughts??
A thin plastic screen protector is not going to stop it from cracking due to an impact, it will stop scratches at most. Your case has a lip at the front to try and mitigate against screen damage when dropped but that isn't necessarily going to stop damage caused by a frontal impact.
Is it possible you banged into the corner of a table and unluckily hit your screen?