My thought is that we cannot truly understand the Holy Spirit's work in the Christian life without first understanding what is the salvation of the Christian. A.W. Pink talks about the work of the Holy Spirit and that essentially if we could somehow do it all by ourselves as if all we needed to do is to believe in the gospel of Jesus Christ and have our faith rest in Him in order to escape hell and to go to heaven then there is really no need of the Spirit (Pg. 45 in the baker edition of the Holy Spirit). I would also add that if all we needed is just a little push or prodding then there would still be no need of the Holy Spirit.
Christ did not die to save us from Hell, although that is not void from the gospel. However He died that we by faith may attain to His nature which is wrought in us by the Power of the Holy Spirit. Has Pink says, "If the salvation which He has provided is a deliverance from sin and self-pleasing, from worldliness and indulging the lust of the flesh, and the bestowing of a nature which desires and determines to live for God's glory and please Him in all the details of our present lives - then it is clear beyond dispute that none but the Spirit of God can impart a genuine desire for such a salvation." Again this alludes to the question what is true freedom? Is freedom a thing that says I can choose between two choices without any external pursausions (spelling?) or is freedom that scripture speaks of a freedom from the bondage of sin. Well if we say freedom is that I might choose between two equally uncoerced choices - then the question is is God free? I would argue no. However scripture does not state that is what true free-will (freedom) is. (Romans 5) Because Adam sinned all of his posterity(spelling) have been plunged into death and are now born naturally totally depraved (Psalm 51:5, 58:3). Jesus says that if you sin then you are a slave to sin. Romans 3 says that all men are hate God (paraphrased). Essentially the idea is that there is something wrong with our nature with our total being. In in Romans 5 we see the two covanental ideas that in Adam all die but in Christ recieved by grace through faith all are made righteous and are given life. So my point is that true freedom is not having the ability to choose between two choices but is freedom from the bondage of sin from a life that hates God and wants nothing to do with God to a life that loves God and longs to do His good work (Philippians 2:12-13). And by this we need the Holy Spirit to do. If we did not then it would be useless for us to say that the Holy Spirit in the life of the believer is necessary.
I think Herman Hoeksema says this very well in his work "The Wonder of Grace." He says, "Saved by grace! Delivered from wrath, guilt, damnation, corruption, and death - all by grace! Clothed with righteousness, holiness, life, and glory - by grace only! Translated into light, from death into life, from shame into glory, from hell into heaven - all by the power of God's wondrous grace! And all because of the eternal, sovereign love of Him Who chose the things that are not to bring to nought the things that are; that no flesh should glory in His presence!" (Pg. 15)