In Protestant faith is one's old self dying on the cross with Jesus symbolic, or the actual assumption of a new Eternal life? Many years ago I accepted Jesus as my savior in a small Baptist church. Up until that time I had never felt any guilt over sinning. Since that day though I have a guilt feeling every time. Years ago in a sermon the preacher said that the old person was crucified with Christ when he died on the cross, because Jesus assumed all sin of everyone who accepted him, and gave their sin burden to him. At the time he quoted a scripture which said that we became a new creature when we accept salvation. I found the scripture some years later; it is:

note: All scripture is quoted from the King James translation.


  2nd Corinthians 5:17  So that if any one is in Christ, that one is a new creature; old things have passed away; behold, all things have become new.


For many years, especially; as a child, and throughout my teens; every time I messed up I always wondered If I was really saved, since I was sinning again just as I had before. I cannot tell you how many times I have asked Jesus to save me again.

Recently I used a new study lesson which has caused me some deep self examination, because of these scriptures:

Rom 7:18 through 20  


  For I know that in me (that is, in my flesh) dwells no good thing. For to will is present with me, but how to perform that which is good I do not find. For I do not do the good that I desire; but the evil which I do not will, that I do.   But if I do what I do not desire, it is no more I working it out, but sin dwelling in me.


So I went back and restudied this scripture:


  John 17:2  As thou hast given him power over all flesh, that he should give eternal life to as many as thou hast given him. 


Then the next verse jumped out at me:


  John 17:3  And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent. 


At the end of the lesson was these  verses:


  Rom 7:24 &amp; 25  O wretched man that I am! who shall deliver me from the body of this death? I thank God through Jesus Christ our Lord. So then with the mind I myself serve the law of God; but with the flesh the law of sin. 


Taking both John 17:3 and Romans 7:18 through 23, Did we begin our new eternal life at  salvation, but will not be able to escape the sin nature we got from  Adam and Eve gaining the knowledge of good and evil until physical death?
First of all, it's good that you feel "guilty" when you sin, that means your conscience has become much more active upon receiving the Lord. However, there is no need to dwell upon the fact of your sin afterwards, as Christ has died for us already and His blood washes us of all sins


  Heb. 7:27  Who does not have daily need, as the high priests do, to
  offer up sacrifices first for his own sins and then for those of the
  people; for this He did once for all when He offered up Himself.
  
  Heb. 9:12  And not through the blood of goats and calves but through
  His own blood, entered once for all into the Holy of Holies,
  obtaining an eternal redemption.
  
  1 John 1:7  But if we walk in the light as He is in the light, we have
  fellowship with one another, and the blood of Jesus His Son cleanses
  us from every sin.
  
  1 John 1:8  If we say that we do not have sin, we are deceiving
  ourselves, and the truth is not in us.
  
  1 John 1:9  If we confess our sins, He is faithful and righteous to
  forgive us our sins and cleanse us from all unrighteousness.


Note that 1 John is an epistle written to believers, so that implies that though we have been saved, we may still sin from time to time. Therefore just apply the blood of Christ, you are doing it right! :)

However, we can overcome our flesh and sin, and the answer lies in the following verses:


  Rom. 6:6  Knowing this, that our old man has been crucified with Him
  in order that the body of sin might be annulled, that we should no
  longer serve sin as slaves;
  
  Rom. 6:11  So also you, reckon yourselves to be dead to sin, but
  living to God in Christ Jesus.
  
  Rom. 6:12  Do not let sin therefore reign in your mortal body so that
  you obey the body’s lusts;
  
  Rom. 6:13  Neither present your members as weapons of unrighteousness
  to sin, but present yourselves to God as alive from the dead, and your
  members as weapons of righteousness to God.
  
  Rom. 6:14  For sin will not lord it over you, for you are not under
  the law but under grace.


Here it says that we need to know that our old man has been crucified with Christ (Rom. 6:6) as a divine fact, that is, we reckon by faith that we are dead to sin, which means that in the face of sin, we are dead. That verse mentions that the result of our old man being crucified  is that our body of sin is annulled, literally meaning "unemployed, jobless, inactive". By standing upon this fact in faith, we overcome sin. The way to do it is presented in Romans 8:


  Rom. 8:1  There is now then no condemnation to those who are in Christ
  Jesus.
  
  Rom. 8:2  For the law of the Spirit of life has freed me in Christ
  Jesus from the law of sin and of death.
  
  Rom. 8:3  For that which the law could not do, in that it was weak
  through the flesh, God, sending His own Son in the likeness of the
  flesh of sin and concerning sin, condemned sin in the flesh,
  
  Rom. 8:4  That the righteous requirement of the law might be fulfilled
  in us, who do not walk according to the flesh but according to the
  spirit.
  
  Rom. 8:5  For those who are according to the flesh mind the things of
  the flesh; but those who are according to the spirit, the things of
  the Spirit.
  
  Rom. 8:6  For the mind set on the flesh is death, but the mind set on
  the spirit is life and peace.
  
  Rom. 8:7  Because the mind set on the flesh is enmity against God; for
  it is not subject to the law of God, for neither can it be.
  
  Rom. 8:8  And those who are in the flesh cannot please God.
  
  Rom. 8:9  But you are not in the flesh, but in the spirit, if indeed
  the Spirit of God dwells in you. Yet if anyone does not have the
  Spirit of Christ, he is not of Him.
  
  Rom. 8:10  But if Christ is in you, though the body is dead because of
  sin, the spirit is life because of righteousness.
  
  Rom. 8:11  And if the Spirit of the One who raised Jesus from the dead
  dwells in you, He who raised Christ from the dead will also give life
  to your mortal bodies through His Spirit who indwells you.
  
  Rom. 8:12  So then, brothers, we are debtors not to the flesh to live
  according to the flesh;
  
  Rom. 8:13  For if you live according to the flesh, you must die, but
  if by the Spirit you put to death the practices of the body, you will
  live.


Verse 13 is quite clear that the way to put the flesh to death is by the Spirit, and the prior verses in Rom. 8 gives in detail how that works.

From Romans 7 (which you quoted), we see that we still have the flesh, and even Paul himself struggled with his flesh, and that there is a "law" in his members, that is, in his flesh, which works against the law in his soul that wants to follow the righteous law of God. Note that we can interpret the "law" in his flesh and in his soul not as something to be followed, but as like a natural law, such as the law of gravity. Therefore as long as we are in our flesh, we will constantly fail to please God and overcome our sins (Rom. 8:3-8). However, we see that we as believers are in Christ Jesus (Rom. 8:1), and that we have received the "law of the Spirit of life" upon our salvation, which is stronger than the law of sin in our flesh. The way to overcome, then, is to live according to our spirit (Rom. 8:4), set our mind on the spirit (Rom. 8:6). The Spirit of God which dwells in our spirit is the factor that overcomes the sins in our flesh (Rom. 8:9). Practically speaking, when we set our mind on our spirit, we are victorious and will not sin because of the law of the Spirit and life. However, whenever we set our mind to our flesh, we will fail. Therefore to overcome the flesh and sin, we must exercise to set our mind on our spirit (1 Tim. 4:7-8, Acts 24:16).

And finally, we have 


  Gal. 2:20  I am crucified with Christ; and it is no longer I who live,
  but it is Christ who lives in me; and the life which I now live in the
  flesh I live in faith, the faith of the Son of God, who loved me and
  gave Himself up for me.


The result of being in our spirit is that our being crucified with Christ becomes a reality. It is no longer us that try to be good and follow the law, but that Christ in us (in our spirit) would work out all things. We cannot overcome sin, but Christ can. Just allow Him to be the overcoming One in us