I've been coming across some apologetics material lately, comparing 2 different schools of thought, both rooted in Reformed theology. Let's take a look...
1. Classical, or evidential - rooted in Benjamin Breckenridge Warfield, and modern advocates like RC Sproul, this school uses reason to argue with unbelievers for the existence of God and authenticity of the Scriptures, using evidence. It assumes there is enough sound reason with the unbeliever to communicate a convincing argument to him, which can at least set him to wondering.
2. Presuppositional - finding its roots in Abraham Kuyper and its full incarnation in the late Cornelius Van Til and Greg Bahnsen, this school says you can't use reason as a standard to prove God's existence or the truth of Christianity, because that would make reason the ultimate standard for truth instead of Christ. But if you start by presupposing (thus the name) the truth of God's revelation in the Christian Scriptures, you then have a proper perspective of reason from which to conclude other things God has revealed.
The classical school critiques the presuppositional school for simply begging the question of God's revelation, providing no logical support for it.
Personally, I'm firmly in the "undecided" camp, here. I think there's some truth in both, but the question seems to hinge on how sound our reason is. It is fallen, and thus, as the presupp-ers like to point out, "The man without the Spirit does not accept the things that come from the Spirit of God, for they are foolishness to him, and he cannot understand them" (1 Cor 2:14). They take this verse as a description of the condition of fallen reason. Incapable of discerning spiritual things. Okay, but the image of God within us (reason being part of that image) is not obliterated in the fall. It's in pieces and may not work well, but unbelievers can add, run experiments, even send ships into space it seems. They have enough reason left within them, and God communicated clearly enough for them to get it. But they have rejected it, and only THEN did their thinking become futile (Rom 1:19-21).
I would compare this to discussions about how effective the sacraments are. I believe they are means which communicate grace to the believer. They nourish a pre-existent faith, they don't create it. Yet without it, we have little support for our faith (unless God nourishes us through other means, which He can and does do). Same with how effective reason is in one's coming to faith in Jesus. Reason does have a helping role to play, but it isn't the establishing standard and starting point.
That probably puts me in the presupp. camp, essentially, but I'm quite uncomfy with many of their derisions of classical folks.
When talking with an unbeliever, pray for them, try to communicate what you believe and why, and feel free to use reason in the discussion if you sense that is a primary standard for him. You need to answer people's objections. This is a means of evangelism God has given us to use, not despise. "To those not having the law I became like one not having the law (though I am not free from God’s law but am under Christ’s law), so as to win those not having the law" (1 Cor 9:21). You can easily translate this: to those who take reason as the standard for their beliefs, I became as one who does the same. Of course that might lead you to Eccleasiastes 2 with them (reason alone will lead to nihilism), but at least you're talking with them.