Which side is winning?

Hello everyone, I saw this game yesterday. White was initially winning (due to the pass pawn) but I figured out this position for Black that would change the situation. According to my matches with the computer last night, it is a draw. But I think Black should have an advantage here, eventhough White still has a few dirty tricks left. So my question is which side is winning. It's White to move.

As you can see, Black is threatening White with checkmate in one by moving the Rook on C file to H file (RC1 - H1). White's only chance to prevent this mate is to move the pawn G2 foward. 

There are 2 cases, pawn moves 2 squares foward and or only 1 square. 

Case2: Pawn moves 2 squares: En Passant would weaken the pawn structure of White, but prevent the threat of Black Pawn Promotion later. I haven't tried this.

Case1: Pawn moves only 1 square: I had tried this whole last night, but still cannot figure out the win for Black. My best try is to get a stalemate with 1 pawn up.

Please help me. And sorry for my bad English.

Case 1: Stalemate. No matter what I do, it is still a draw.

draw