I'm joining the discussion late, not because of lack of interest but because time has been short.
It may be helpful to note the following discussions of this verse, in addition to those already noticed:
What did Jesus mean by τὴν ἀρχήν in John 8:25? Caragounis, Chrys C. ; Novum Testamentum, 2007, vol. 49, no 2, pp. 129-147. (I'm not sure how matters stand elsewhere, but here in Australia I was able to obtain an electronic copy of this article through a public library; i.e. access isn't restricted to those able to get to a university or theological library.)
George R. Beasley-Murray, John, 2nd edition, p125
I especially recommend the Caragounis article as being masterly; my working definition of a masterly article is one where, even if I end up disagreeing with its conclusions, I learn new data and am forced to a clearer understanding of the boundaries of possible interpretation.
In case they may be of some help, I'll add the following notes made for myself and students which I sketched out quite a while ago:
Τὴν ἀρχὴν ὅ τι καὶ λαλῶ ὑμῖν; As Chrys C. Caragounis wrote, "The answer which Jesus, according to John 8:25, gave to the Jews has at all times been regarded as problematic." (What did Jesus mean by τὴν ἀρχήν in John 8:25? Caragounis, Chrys C. ; Novum Testamentum, 2007, vol. 49, no 2, pp. 129-147) His article is recommended as a clear exposition of the problems and possibilities in understanding this verse. Beasley-Murray says of this second part of the verse, "V 25b is the most obscure sentence in the Gospel and the most uncertain how to translate." (George R. Beasley-Murray, John, 2nd edition, [etc] p125)
The difficulties of this sentence revolve around a number of questions: What is the correct text? What is the correct division of the words? What is the meaning of the words? What is the correct punctuation? Is any word or number of words to be supplied in order to fill out the sense?
The textual question arises because the Papyrus Bodmer II (P66) reading gives a readily intelligible sentence; however, the reading is unique, and for this reason must be rejected.
The matter of word division arises because ὅ τι may be read as ὅτι.
The question of meaning arises because τὴν ἀρχήν may be understood in different ways.
The question of punctuation arises because some editors have taken the words as a question, others as a statement.
Beasley-Murray gives six translational options, and variants as well. He acknowledges the proponents of each understanding and discusses their merits in a brief discussion on pages 125-126 to which the student is referred. The translational options he identifies are these:
'Why do I speak to you at all?'
'Primarily what I am telling you.'
'(I am) from the beginning what I tell you.'
'(I am) what I have been telling you from the beginning.'
'I told you at the beginning that which also I am speaking to you (now).'
'I am the beginning, that which I am saying to you.'
The last of these is based on the Latin versions, which rest on a misunderstanding of the Greek, and needs no consideration. The second-last is the rendering of Bruce (194) and is based on the Papyrus Bodmer II (P66) reading, not on the text as given in the UBS edition.
It is not the intention of this discussion to resolve the issues surrounding these words, about which certainty seems beyond our attainment. What follows, then, is merely an adumbration of some of the linguistic matters that arise, given with the intention merely to indicate some of the parameters within which we must frame an answer to these difficult words.
Firstly, τὴν ἀρχήν. The phrase is not used as the object of a preposition or verb so that the meaning 'the beginning' is of no relevance here. What is required is an understanding of τὴν ἀρχήν here as an adverbial accusative. The meaning 'at all' is well-established from classical usage. This sense may not seem obvious, but if we think of the English phrase "to begin with", its development of the sense 'at all' may not seem so difficult. (It is this sense that is drawn upon by the first of the translational options noted by Beasley-Murray, 'Why do I speak to you at all?') But it may also be used with temporal reference to mean, according to context, 'in the beginning', 'at the beginning', or 'from the beginning'. But here the student should take careful note of Caragounis' comment that "The notion conveyed in English by the prepositions from, at, or in in the phrase 'from/at/in the beginning' is an added notion in order to make English sense of the construction." (It may help to think of τὴν ἀρχήν as an accusative of respect, 'in respect of a/the beginning' - that is, of itself the phrase does not indicate time from, at, or in.)
Secondly, how is ὅ τι to be divided, and understood? If taken as ὅτι, it may be understood as a conjunction, 'that'. If we supply something like 'to think', the understanding of ὅτι as a conjunction allows the sense to be taken as '... [to think] that I am speaking to you!'. But ὅτι may be taken to mean 'Why?', and this understanding has informed some of the translations. Caragounis, however, points out that, in the New Testament, ὅτι is used in direct questions only in Mark (see Caragounis, pages 140-141, with footnote 38). ὅ τι, however, may be read, and understood as 'that which'. This understanding underlies translations such as '(I am) from the beginning what I tell you' and '(I am) what I have been telling you from the beginning'; both of these supply εἰμί as being understood, but differ in taking the τὴν ἀρχήν with the understood 'I am' or with the following clause.
The third and final point to be noticed here is that it may be felt difficult to take τὴν ἀρχήν in the sense 'from the beginning' when the verb in this clause is in the present tense, as in English to say 'From the beginning I am speaking to you...' is awkward, English idiom prefering rather 'From the beginning I have been speaking to you...'. But English idiom ought not distort our perception of the Greek. "The present indicative can certainly be used of an action that began at some point in the past and continues in the present, that is, it is equivalent to the English progressive perfect." (Caragounis, page 145.)
This brief note will suffice to indicate that the meaning of these words is uncertain, and the issues to be resolved are complex and interlocking. Caragounis' article is particularly recommended for its full and clear enunciation of the difficulties and for its breadth of research.