Unfortunately there's a lot of confusion over that passage from 1 Corinthians because English doesn't really have a good translation of what's being said in the Greek. What Paul is contrasting here is the soma psuchekos and the soma pneumatikos. This word psuchekos is an adjective form of psuche, usually translated as "soul", and so soma psuchekos means something like "soulish body". So the contrast is between the "soulish body" and the "spiritual body".
Now, these adjectives have nothing to do with the material composition of the body, this should be common sense since obviously the present body isn't comprised of some sort of soul-stuff. Rather it speaks instead of the sort of operating or animating principle of the body; the present body is governed by the soul, it is animal, base, mortal, dependent upon the animal desires and appetites. However, in the resurrection the body is instead "spiritual", or perhaps better put Spiritual. In the resurrection the sort of life we have is from the Holy Spirit, it is a glorified body, a transformed body, an immortal body, an incorruptible body.
Compare with what St. Paul writes in Romans 8:11, "If the Spirit of him who raised Jesus from the dead dwells in you, he who raised Christ Jesus from the dead will also give life to your mortal bodies through his Spirit who dwells in you."
It is the Spirit who quickens, who gives life to our mortal bodies in the resurrection. And so, as Paul writes, "this mortal must put on immortality, this corruptible must put on incorruption." There is a transfiguration of the body, from mortal to immortal, from corruptible to incorruptible. From, as Paul again writes in Philippians chapter 3:21, "[Christ,] who will transform our lowly body to be like his glorious body, by the power that enables him even to subject all things to himself."
The resurrection is physical, as it is of the body. It is not us going from physical to non-physical; but the physical body going from "soulish" to "Spiritual"; from mortal to immortal, from the present order of things laboring as they are under sin and death to the full glorious estate of the future world. For we look forward to the resurrection of the body and the life of the Age to Come, for God will make all things new, as all creation which now labors under bondage of sin and death shall be set free (Romans 8:18-24), made whole, and glorified in the beatifying Light of God in that glory which is to come (Isaiah 65:17-25, Revelation 21:1-6).
-CryptoLutheran