Obi,
So, assuming the biblical story of Adam and Eve and the entrance of sin into the world is correct, and we have basically have a human race that is in open rebellion against it's Creator, let me proceed from there. And let me define sin as anything that doesn't fit the "Love the Lord your God with all your heart, mind, and soul, and love your neighbor as yourself", which is basically a summary of the ten commandments and I submit, the root of the sin issue. (Sin would then be putting yourself and your interests before others, or worshiping, treasuring, valuing something or someone more than God.)
So if this is basically God's law for human relationships, that we are to hold God as of ultimate worth above everything else, and love our neighbors as ourselves, then breaking a such a law requires justice. As humans on earth we are all familiar with this concept. If you break a law, justice is required. If God is all powerful, hypothetically speaking "could" He forgive without justice? Well, let me submit that this may be the wrong question. What about the question "would" or "should" he forgive without justice?
If God were to forgive without justice, would He be a good God? Consider a rapist and his victim. If God were to simply forgive the rapist with no justice, He has wronged the victim. Where is the justice in that? If God were to punish the rapist with no mercy, who would follow God? If by the definitions above we have all sinned, then the justice that God tells us is required is death, and who would follow God if he were completely just with no mercy? Might as well collectively stick it to God as best we can. But what if there was a way to both provide justice, and mercy? This is where Jesus dying on the cross comes in. If Jesus kept God's law for human relationships, and thus was "perfect" he can then represent the human race where Adam failed. Then he willing takes the punshiment that the human race deserves, mercifally giving members of the human race an opportunity to be reconciled to God. Justice has been carried out, the "blood sacrifice" made. From the rapist's perspective, he realizes his sin carried the Son of God to one of the most horrible deaths imaginable, and yet witnesses God's mercy in allowing him forgiveness of his sin because justice has been carried out on the Son of God. The victim also can see God's justice, though here I fully expect people will argue with me. The victim (who by definitions above) is not without guilt in other areas in their life, though the rape was not the vicitm's fault in any way. If the vicitm of the rape has been forgiven by God and understands God's justice being appeased at the cross and his offer of mercy, then she can accept that justice has been done (having seen her own lawbreaking send the Son of God to the cross), and her view of her attacker changes because she sees that as she has been forgiven she is now enabled to forgive and that God has offered forgiveness to that person. If we are all sinners, we are all expected to behave like sinners, thus seeing God take the justice part out on his Son and extend us mercy, allows us to do so for others, even those who have wronged us.
I relate this case study as I know a girl who this has happened to and this is how she explains God's justice and mercy.
Hope this helps explain things some Obi.