でね is the continuative form of だ plus the 語尾 ね. (Works just as well with the continuative of any other verb.)

で is usually used to connect to phrases, but when the speaker is too excited about the first part already, s/he wants to affirm it with ね. In fact, でね can be used at the beginning, in the middle, or at the end of a sentence.

At the beginning, it could be interpreted as 「それで、…」.

In the middle, it really just is ascertaining the versatility of ね, which is used as interjection (and is expected to be confirmed with うん).

At the end the use is the same again, just the rest of the sentence is being omitted.

Only in the last case, the listener has to read into the speaker's mind of what the conclusion of the 「…で」 part should have been. E.g.

俺のこと嫌いって言ってね、本当にムカつくんだよ。
She told me she hated me, that old windbag.

becomes

俺のこと嫌いて言ってね。まぁ、とにかく、結婚するか今のとこは分からない。
She told me she hated me, but... In any case, I'm not sure we will actually get married.

でね is the continuative form of だ plus the "interjectory particle" (間投助詞) ね. (Works just as well with the continuative of any other verb.)

で is usually used to connect to phrases, but when the speaker is too excited about the first part already, s/he wants to affirm it with ね. In fact, でね can be used at the beginning, in the middle, or at the end of a sentence.

At the beginning, it could be interpreted as 「それで、…」.

In the middle, it really just is ascertaining the versatility of ね, which is used as interjection (and is expected to be confirmed with うん).

At the end the use is the same again, just the rest of the sentence is being omitted.

Only in the last case, the listener has to read into the speaker's mind of what the conclusion of the 「…で」 part should have been. E.g.

俺のこと嫌いって言ってね、本当にムカつくんだよ。
She told me she hated me, that old windbag.

becomes

俺のこと嫌いて言ってね。まぁ、とにかく、結婚するか今のとこは分からない。
She told me she hated me, but... In any case, I'm not sure we will actually get married.