Not all these theories are wrong by any means. Christ did pay a ransom (Not to Satan, but to God's justice), Christ did rise as Victor from the grave and the cross should melt our hearts and cause us to repent. But none of them are sufficient unless there is also an understanding that Christ was also receiving on our behalf the rightful penalty for our sins, 'That He might be just and the justifier of the one who believes in Jesus.'
So it is that one can find some of the FCFs talking about ransom theory at one moment and Penal Substitution the next.
The cross is 'foolishness to the Greeks and a stumbling-block to the Jews.' The latter is brought out very clearly in Justin Martyr's Dialogue with Trypho the Jew.'
Trypho recognizes that the Christ must suffer, but he cannot bring himself to believe that He would be crucified, since the OT law teaches that anyone crucified is under God's curse (Deut. 21:23):
'Then Trypho remarked, "Be assured that all our nation waits for Christ; and we admit that all the Scriptures which you have quoted refer to Him. Moreover I do admit that the name of Jesus, by which the son of [Nun] was called, has inclined me very strongly to adopt this view. But whether Christ should be so shamefully crucified, this we are in doubt about. For whoever is crucified is said in the law to be accursed, so that I am exceedingly incredulous on this point. It is quite clear, indeed, that the Scriptures announce that Christ had to suffer; but we wish to learn if you can prove to us whether it was by the suffering cursed in the law' [Sect. 89]
Justin begins by assuring Trypho that Christ was not cursed for His own sins: 'Though a curse lies in the law against persons that are crucified, yet no curse rests on the Christ of God, by whom all that have committed things worthy of a curse are saved' [sect. 94]
'For the whole human race will be found to be under a curse. For it is written in the law of Moses, "Cursed is everyone that coninueth not in all things that are written in the book of the law, to do them." And no one has accurately done all, nor will you venture to deny this........But if those who are under the law appear to be under a curse for not having observed all the requirements, how much more shall all the nations appear to be under a curse who practise idolatry, who seduce youths, and commit other crimes' [sect 95]
Then Justin reaches the crux of his argument, where he explains that the reason why our Lord was crucified is that the curse which rested on us for our sin was transferred to Him.
'If then, the Father of all wished His Christ for the whole human family to take upon Him the curses of all, knowing that after He had been crucified and was dead, He would raise Him up, why do you argue about Him, who submitted to suffer these things according to the Father's will, as if He were accursed, and do not rather bewail yourselves?' [sect 95, emphases added]
This amounts to a clear statement of penal substitution. Although Christ was innocent, He bore the curse due to sinful humanity, enduring in His death the punishment due to us. Several others of the ECFs explain this doctrine on the basis of the 'curse' vocabulary of Gal. 3:13 and Deut, 21:23, including Eusebius of Caesarea ('Proof of the Gospel, bk.10, ch.1) and Hilary of Poitiers (Homily on Psalm 53 [actually 53], sect. 13).