This is a fascinating discussion--I suspect many readers might be sorry to see it disappear from public view (even if we don't feel competent to add anything to it ourselves).
I grant that the discussion could readily segue into theology, but the basic puzzle here is not so much theological as contextual--viz. what could ορισθεντος υιου θεου εν δυναμει κατα πνευμα αγιωσυνης εξ αναστασεως νεκρων possibly mean in the context of the work in which it appears?
Let me offer an analogy. If you were reading Darwin's Origin of Species, and you found a sentence that appeared to mean "The world was created in 4004 BC," you'd be certain you'd misunderstood it--not for any theological reasons, but purely for contextual ones: because such a statement would run counter to the whole context of the author's argument in the book.
In the present passage I think the puzzle is somewhat similar. At first glance the above clause may appear to mean something like "appointed Son of God when he rose from the dead." But, whatever the theological truth may be, it's hard to believe that such a statement could have been written in Romans (or in any other Pauline letter).
For what it's worth, the major commentators are divided between two explanations:
1. Those who defend the rendering "declared" usually cite Chrysostom's paraphrase δειχθεντος, αποφανθεντος. If a 4th-century native Gk speaker with an unparalleled sensitivity to language felt that ορισθεντος could mean something like "proved to be" or "marked out as being," who today is qualified to say that it could never have had such a meaning in the 1st century? In that case, "the word itself does not determine the meaning either way: it must be determined from the context. But here the particular context is also neutral; so that we must look to the wider context of St. Paul's teaching generally. Now it is certain that St. Paul did not hold that the Son of God became Son by the Resurrection.... At the same time he did regard the Resurrection as making a difference... in the visible manifestation of Sonship as addressed to the understanding of men (cf. esp. Phil. ii.9...). This is sufficiently expressed by our word 'designated.'" (Sanday & Headlam, pp. 7-8).
2. Those who oppose the rendering "declared" argue that "no clear example, either earlier than, or contemporary with, the NT, of its use in the sense 'declare' or 'show to be' has been adduced." In explaining the clause, they usually lay stress on εν δυναμει (which they take to modify υιου θεου). Christ may or may not have been ορισθεντος Son of God in other ways at other times, but he was ορισθεντος Son of God ΕΝ ΔΥΝΑΜΕΙ at the resurrection. (So, e.g., Cranfield, vol. 1 pp. 61-62). These commentators appear to be substantially in the majority; it's interesting that they've had so little influence on the English translations.
At any rate I have a distinct impression that the word ορισθεντος is meant to startle the reader. Everything in the letter has been plain sailing up till this moment, and then, suddenly, bang!--what does this strange thing mean? It's as if a little language bomb suddenly explodes under your feet at the mention of the resurrection. That's something that the English translations don't convey: they smooth everything out into the comfortable prose of a newspaper editorial.