Good Deeds the Fruit of Regeneration or the Indwelling of the Holy Spirit?

[TheThirdandReformedAdam]

This is probably an extremely silly and simple question to many (but, then again, I'm an extremely silly and simple guy). I am a little confused concerning New Covenant promises on the internalization of the Law. So, as I presently understand Jeremiah's prophecy in 31:33, this internalization of the Law is the obedience of God's children resulting from the indwelling of the Holy Spirit (Romans 8:13,14; Gal. 5:16-23; Rom. 7:6). So far so good. Except, as I was reading through a section in Wayne Grudem's systematic theology on regeneration, I noticed he cited texts like Ezekiel 36:26-27 as evidence that New Covenant obedience would be the result of regeneration (where a new heart (as well as a new spirit) is said to be the agent which would cause the New Covenant members to walk in God's statutes and be careful to observe His ordinances).
I understand that we are (in logical ordering) first regenerated by the Holy Spirit, then come to saving faith as a result, and finally are sealed by the Holy Spirit. My confusion is this: does the New Covenant Christian produce good works solely because of the indwelling of the Holy Spirit, or does the regenerated heart which allowed for faith somehow play a role as well? Does regeneration only occur in order to produce faith and, as a result, only participate in the 'law written on the heart' via its foundational position in bringing the elect to Christ? I guess I had always thought of regeneration as nothing more than the necessary prerequisite for faith, and the indwelling of the Holy Spirit as the sole reason for the fruit of righteousness in the Christian life. I feel like I'm really misunderstanding something.

 

[Peairtach]

All the exhortations of Scripture teach that the regenerate soul interacts with the Holy Spirit in making use of the means of grace to do good works, and make progress in sanctification and obeying the law. All the glory goes to God. See e.g. the Chapter in the Westminster Confession of Faith on "Good Works"

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[Dachaser]

The Lord grants to usa new nature that wants to now please God and obey Him, but we need the Holy Spirit to actually enable and give us spiritualempowering to do that, as we can desire to please and serve God, but the flesh is still weak, and Jesus said unless we abide in Him and walk in the Spirit...