You have used the TULIP as an acrostic to roughly describe your theological understanding. Though I don't care much for that approach, I know a number of Calvinists and Reformers have used it in the past. It seems as good a place to start as any...
Here is yours repeated:
T-- Total Depravity -- all have sinned. None are righteous.
U -- Unconditional Election -- Not possible. There must be a condition otherwise it is arbitrary. God is not Arbitrary.
L-- Limited Atonement-- Not Biblical, but a necessary linchpin to hold together the other four point.
I -- Irresistible Grace -- You bet. It is irresistibly thrust upon all men. It is, however, rejectible grace. If you receive it you will be saved, if you reject it, you will be damned. But the same grace which results in one man's salvation may result in the next man's damnation.
P-- Perserverence of the Saints -- Eternal life is eternal. Once you have it, you can't lose it. Otherwise it is not eternal.
It was a bit ambiguous but appears that you agree with T, I, P and grudgingly L. Even your agreement with I seems to be conditional and not what I would normally categorize as irresistable grace. Your strongest disagreement is U, the idea that God elects those whom He saves.
As I have posted previously, I believe there is more than one type of grace (common grace and saving grace). The saving grace is irresistable (man must respond) but the common grace is that which maintains some semblance of beauty, restraint, and happiness in the lives of sinners and believers alike. Your idea that God's grace damns an unbeliever does not seem to agree with Scripture as far as I can tell. Can you give scriptural basis for this belief?
The aspects of TULIP that I support (in general) is T, U, I, and P. The limited atonement is traditionally misunderstood so I prefer to use a statement more like:
Christ death is sufficient to cover all sins but efficacious only for those who God calls.
We seem to disagree primarily on the topic of election. I don't understand how you can adhere to total depravity and yet not accept election. If man is totally depraved, it seems to follow that man cannot choose God on his own. There is a substantial amount of scripture that supports the idea of an elect (it is used at least 8 times in the NASB) and that Man is dead in his sin. I would admit that these are hard truths, but they are scriptural and follow a logical understanding of God's sovereignty.
The hardest aspect of this view is the issue of sin. Where did it come from? Why did God allow it to enter this world? If He is truly sovereign, does it imply that God is the "author" of sin?
I will end here because I wish to get your response before continuing the discourse. It may be that we have much more to discuss before touching on the issues of sin...
You are correct that I do not believe in "unconditional" election. God must have a reason to elect one man for salvation and another for damnation. I believe the bible teaches that the condition is Belief in Christ foreknown from the foundation of the earth.
As far as common grace and Saving Grace goes, I think that the term Common Grace as used by Calvinists has nothing to do with soteriology, but has to do with God's patience with sinners. Fine, if that is Common Grace, then I have no issue that there are two kinds of grace. however when it comes to soteriology and when it comes to the issue of salvation, there is only one grace and that grace is extended to all men and the same grace that will save one man who receives it will damn the person who rejects it. This seems to make the most sense both from a scriptural standpoint and from a logical standpoint.
I believe it is very well expressed by Donald Bloesch as follows:
It is still possible, however, to speak of irresistible grace even in the case of the one who falls away from grace. Grace still triumphs but now in the form of wrath and judgment. The love of God necessarily becomes destructive to the one who rejects this love, but it is never withdrawn from the sinner, even from the apostate. He meets his deserved retribution not despite the grace of God but in the face of grace and at the hands of grace.
When we say that grace is irresistible we mean not only the first entry of grace into our lives but also the fact that grace cannot ultimately be defeated. Grace is irresistible in the sense that we cannot act either for, with, or against it until it is showered upon us. We are dead apart from grace (Eph. 2:5). We can swim against the stream of grace but only on the basis of grace and then only for a time. It is true that God may withhold his grace from us, but this too is only for a time. God's grace cannot be permanently thwarted; it will finally have its way in the life of man, though this may mean man's condemnation and not his salvation. Perhaps it is more proper to speak of efficacious or effectual grace than irresistible grace since man, even after having been exposed to grace ever and again, inexplicably but incontestably descends into the depths of absurdity and tries to defy the grace of God. But when in his folly he denies his salvation, grace is still triumphant though in a different way, and when he gladly acknowledges the blessing assured to him, he does so because he is irresistibly drawn to the love and light of Jesus Christ.
Against the older Calvinists we maintain that grace will eventually be given to all, that it is not reserved for a select group of the elect. Against the Arminians we contend that grace cannot be permanently thwarted or resisted, that grace is inescapable and unrelenting. Against them too we hold that grace does not simply dispose the corrupt will toward the good but actually transforms man's will so that he seeks to do the good. Our position is that grace is both universal and sovereign even where people defy it.
Donald G. Bloesch (1978) Essentials of Evangelical Theology Vol 1 page 206-207
Now to get to your question of why is there sin. Sin is rebellion against the will of God. It is a natural outgrowth of free will. If God created man without the ability to rebel against him, there would be no sin. But God did not create man that way. Now if God has plotted out each action of man from the foundation of the earth and each action of man was in full accordance with the will of God, then no matter what a man did it would not be sin.
Thus it is impossible for sin to exist unless man is truly free to act independent and in opposition to God's will. If it is God's decree that a man act in a certain manner and he acts in that manner, then he is not sinning, but he is doing God's declared will. He is not rebelling against God, but is acting in concert with Him.
So if God commands men not to steal, then we must assume that God really really does not want anyone to steal. And likewise if God commands all men to believe in Jesus Christ, then we must assume that God really really wants all men to believe in Jesus Christ. The fact that they don't proves that either God is a liar, or that men truly have free will.
BTW if you are not a "Calvinist" what are you? Are you a four pointer?