- English does not use a colon in that position. It uses a comma.
- The spoken words should be within quotation marks.
- The quotation itself should be punctuated and written independently of the containing sentence.
She said, "When are you going?"
Addendum (following OP's comment)
Even for some "avant-garde writing", I would follow my point 3 above: if the quotation is a complete sentence, then punctuate and capitalise it as such. I would, however, go further, ans suggest that,; but even if the quotation were not a single sentence because the speaker only spoke a partial sentence, or even only a single word, I would still capitalise and punctuate it as if it were a full sentence, thus indicating that that it is the full text of what was said.
However, if you are asking about using a colon in normal writing (and not in the context of a stylised form of quoting speech), then, no, you capitalise as you would in any continuation of a sentence, namely, only for a proper noun. For example, see:
- the first paragraph of this Addendum.
- the first indented paragraph of the answer from @J.R.