Unfortunately, they haven't walked away because you've stumped them. They've walked away because they realize they cannot reason with you. We have tests and equipment that give us information about electricity. Everyone knows what it feels like to be shocked by electricity or static electricity.  

We have no such tests and equipment for proving God's existence and not everyone has seen, heard, or felt God. According to the most recent research, God is "felt" in the temporal lobes of those susceptible to such things. Just as some people are more able to be addicted to caffeine or nicotine, so are some people more sensitive to stimulation of the temporal lobe, and then reporting a feeling that there is a being in their presence.

As for explaining your belief in God to those who do not share your faith, the intellectually honest response would be, "I know that there is no proof, but I choose to believe in him anyway."

Faith.  You believe in Him because you have faith in him, even though you can not see Him you know he is there because of your faith!

Electricity is a wonderful example. Wind is too, you know it is there you can't see it, but you can feel it.

I think the best way to deal with non-believers around you is to live you life in such a way that they can't help but notice Jesus living in you.

In that area I've just decided to ask God to build bridges between them and I and just to love them and be patient with them...God tells us to be patient with others.  Bless.