First, consider what you would regard as a positive demonstration of God's existence. You might, for instance, imagine a scenario where God appears in the sky (white beard, long robes, and all), everyone else behaves in a manner that leads you to believe they also see him, the six o'clock news reports the event, and so on. Furthermore, this apparition correctly predicts exactly what important events will take place over the next year (deaths of famous people, hurricanes, who will win the Superbowl, etc.). If this isn't good enough evidence, then, as I said, simply supply your own scenario. Call the scenario which you would regard as sufficient, event e.
Now consider statement A, "If I ask God for proof of his existence, then event e will occur". If A is true, then, per the above stipulated conditions, you agree that God exists. That is: if A, then God exists.
So our first premise is: "If, if I ask God for proof of his existence, then event e will occur, then God exists". Provided there is some scenario you would accept as positive evidence of God's existence, this premise is undeniably true.
Second, consider the fact that I will not ask God for proof of his existence. You can accept this as a fact because I am an atheist, so even if I were to say something that might be interpreted as my asking God for proof, I would not be asking God, since I don't believe there is a God for me to ask anything of.
So the second premise is: "I will not ask God for proof of his existence", which is also true.
Now, the argument is as follows. Substituting P for "I ask God for proof of his existence", E for "event e will occur", and G for "God exists", we have:
1. (P -> E) -> G
3. (~P v E) -> G 1, Impl.
4. ~P v E 2, Add.
5. G 3, 4, Modus Ponens
I will leave it to the reader to determine what is wrong with this argument.