Can you inflate a completely flat tire?
You can easily inflate a completely flat tire (provided the tube is still good). Usually, when a tire is completely flat, you have to press the back of the tire so that the valve doesn't recess into the tire so your pump can be attached properly to it. 

With a presta valve, you can use your mouth for this (well, on a clean tube, since the valve stem isn't spring loaded), but with a schrader valve you have to use a pump. 

If it still won't inflate, check the tire and tube for damage and replace accordingly.