Does God's omnipresence extend to hell? One of those attributes of God is his ability to be everywhere at all times.  I'm not debating that it is an attribute of his, I'm just wondering how we know that.

I ask, because I've been going through a question of my own recently - If God is omnipresent, how can hell exist?  After all, hell is by definition, that one place that God is not. But, if God is everywhere, how can there be a place that he is not?

My favorite answer to that question comes from C.S. Lewis' The Great Divorce, in which he describes hell not as a place of fire and brimstone, but rather an infinitely empty, substance-lacking smallness.  The journey from hell to heaven that his characters make is not from "down" to "up" from rather from "small" to "big" and "weak" to "strong." 

I really like using that idea of hell, since it seemingly answers the idea that hell is merely a place that is, itself, so small and insubstantial that it isn't God's lack of presence, but rather its own insignificance that causes God's presence to feel so lacking.

In order to test that assertion, however, I want to make sure that I am correctly stating the postulate - namely that God really can be everywhere at all times. What is its biblical basis, and does God presence exist in hell?
In reading your question, I don't think the issue at hand is God's omnipresence at all. Frankly it's not a terribly important doctrine in the first place and while I think one could make a case for it from Scipture, I think it's a little forced. Much more importantly, the Scripture states the reverse quite plainly, that all things are in and held together by God/Christ.


  Colossians 1:16-17 (ESV)
  16&nbsp; For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him. 17&nbsp; And he is before all things, and in him all things hold together.


This includes hell. The problem with your question is not the doctrine of omnipresence, but the doctrine of hell. You state:


  After all, hell is by definition, that one place that God is not.


But where does that idea come from in the Bible? The problem with hell is that God is there! It is where God pours out his eternal judgement on all things evil. This is a part of his nature and God's wrath will be a very present reality of hell for all eternity. While we can't paint an exact picture of hell, we do have have some fairly vivid and specific descriptions of the way God is involved in punishment:


  Revelation 14:9-11 (ESV)
  9&nbsp; And another angel, a third, followed them, saying with a loud voice, “If anyone worships the beast and its image and receives a mark on his forehead or on his hand, 10&nbsp; he also will drink the wine of God's wrath, poured full strength into the cup of his anger, and he will be tormented with fire and sulfur in the presence of the holy angels and in the presence of the Lamb. 11&nbsp; And the smoke of their torment goes up forever and ever, and they have no rest, day or night, these worshipers of the beast and its image, and whoever receives the mark of its name.”


What is different about it there is that it is a place separated from his grace. Neither the general grace that rains on the just and the unjust alike on this earth nor his specific graces experienced by believers will be experienced there. Folks will be separated from those aspects of God. He is only holding back his hand for a time.