How do the rules apply here!

Using the analysis window to study my opponents options as well as my possible responses I thought Kg3 would be legal since my Knight on f5 couldn't move because it would expose my King.  As it turned out Kg3 was not legal.

I guess I never came across this situation before but now that I have it has triggered thought about the rules.  Two rules apply.  You can't move into check and you can't make a move that exposes your king to a check.  

After some thought I understand why Kg3 isn't legal from this position and I am posting this position for others to consider.  

It's just not legal, because you can take your opponents king first. Therefore you win, because your king is about to die, but the general on the other side died first, leaving you to win. That is somewhat the reason, but I don't explain it too well.

Eh, I think your quibble here is on your definition of "check" in the rule "you can't move your king into check". "Check" does not exactly imply the piece can actually legally move onto that square on the next turn...

Rainxdancers explanation is the same conclusion which I came up with.  Actually it's a simple explanation but I had never given it any thought until it happened.

Interesting, as with my original example it comes down to what happens on the next move.

Actually the rules are pretty straightforward, and the answer has been pretty much given by some others here.

The rules state: "you can't place the king in check", which means you can't move the king into a threatened square. The actual ability or inability of the piece "checking" that square to move doesn't matter.

The fact that the knight can't move has nothing to do with it.

The Black Knight on f5 is pinned to the Black King. The White King certainly can move to g3 or e3. The power of the pin is: Black Knight cannot put his own Black King into check by moving to any square until the White Rook's pin is broken.

Oh no, he can't.

So any piece other than the King could move to those squares. In other words, even if the Knight is immobilized, he still controls those square. OK. Thanks, rooperi.

So you're saying that his last move was Ra5+. Did neither of you notice that you had him in check with YOUR rook?

As you correctly pointed out...It looks like my original comment was incorrect, the Knight was moved in a previous move to block the attacking Rook and my last move was Ra5+.  The condition remains the same though.  And my discovery that the white King could not move to g3 because it would be in check to the Knight on f5 even though the knight was pinned and couldn't legally move is the main subject.

This was also my original thought until I discovered, by using the analysis function of Chess.com, that g3 and e3 were not legal moves.  After thinking it through I understood why the moves were not legal .  This is a situation that I had not given any thought until I was faced with it therefore I wanted to share it with others who may not have faced the condition either.