So was the battery dead? In other words, was the charge light indeed related
to the battery not charging?

What exactly do you mean by "the starter whines"? Is the starter turning the
car over in the sense that you see the belts move, etc? If an engine is
seized and the starter is good, it will not turn over at all - the starter
may, in attempting to start the car, burn out. Or is the starter just
spinning very quickly?
If the car is indeed turning over (you see the belts move, but the car is
not starting), check to see if you have spark.
If you don't have spark, pull the distributor cap off and see if you see the
thing in the middle (called the "rotor") spin. If you don't see if spin, you
may have a broken timing chain (or belt - not sure what a 94 altima has).
If you do see it spin, you may have a broken coil or ignitor (I think Nissan
calls an ignitor something else, but it basically just makes/breaks a
contact, controlling the voltage to the coil - what used to be referred to
as "points". The modern designs are electronic). There are ways of telling
if one is bad so just tell us what you see.

Driving without oil or coolant is a very bad thing - you could have done a
lot of damage (like seizing the engine). Can you turn the crank pulley by
hand or maybe with a wrench? If you can, your engine is not seized. Because
it overheated, it could still be that the head is warped or your headgasget
may have blown. Let's hope this is not the case.

Report back with your findings -- hopefully it is something simple and
cheap.
Remco