***** NOT A TEACHER *****
(1) As you very correctly said, in conversation we might say: I could not sleep because the dogs kept barking all night.
(2) In writing (not speech), we could put this idea in a more elegant manner:
The dogs having barked all night long, I was unable to get any sleep.
With the dogs having barked all night long, I was unable to get any sleep.
(3) I am afraid that your three examples would be labeled "incorrect." In No. 1, for example, the sentence says that the dogs were unable to sleep, so they kept barking all night.
(4) When you have time, please check your books, the Web, or the search box at this website for something called the
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