As a follow up to drybones' post: If the store does allow you to run live ammo through the gun in the store you should leave. There's a very good reason competent gunsmiths use innert ammo when checking an action. Using live rounds can lead to unintended discharges.
These are mass produced items. The manufacturing process has integral QA steps but individual guns are not inspected to the Nth degree. A few will be shipped out with flaws. The only way to guarantee, or even come close to guaranteeing, that you'll buy a working gun is to buy several. You are more likely to get a working gun if you buy two $300 guns than one $600 gun. If you can't (or don't want to) do that, then accept the possibility that the one gun you bought will be going in for service and buy and test well before you need the gun.
That's my take anyway.
As for new in box... it should come with a blue plastic box, a stack of paper, an envelope with some spent brass, a lock, and everything else... in short, it should be new.
NIB == New.
LNIB == Used, but very similar to New.
Everything else should basically be graded NRA "whatever"