In summary of our research on Romans 7:14-25:
Verse 14 Paul is one with his Christian readers and "slave of my own sinful nature". 
Verse 15, Paul is not a non converted man who would sin willfully. 
Verse 17, his actions are the fruit of his sinful nature. 
Verse 18, the "I" is Paul's sinful nature.  
Verse 22, the born again Paul rejoices in the Law of God. 
Verse 23, there is a battle going on in Paul's mind between the spiritual nature and the carnal nature which is destined to death (verse 24). 
The shout of deliverance (v. 25) is followed by Paul's re-affirmation of his predicament: 
it is to show that this is and always will be his condition, even in his converted state. 
He still has this war in himself: 
the old man trying to do his own bad will and the new man trying to follow God. 

The problem is not the law but Paul's sinful nature.
 
But he also shows how he solves his problem: he goes to Christ for deliverance. 
Paul did not obtain deliverance once for all but needs to receive it every day. 
That's why Paul in 1Cor 15:31, writes, 'I die daily'.  
Every day he has to ask God to overpower his old man, his sinful nature. 

All the previous evidence converges toward the fact that, in Romans 7:14-25, Paul, a converted Christian, is fighting, in his own strength, against the old man in him. 
Apart from the Holy Spirit he will always be unsuccessful .