A sentence, even a quoted sentence, should begin with a capital letter. This is true even if the sentence is short and/or not grammatically correct.
He whispered something that sounded like, "It is sunny out."
We are quoting a sentence, so it should be capitalized.
He whispered something that sounded like, "Sunny out."
It's not a complete sentence, but we still capitalize.
We normally capitalize exclamations by the same reasoning:
He shouted something that sounded like, "Hooray!"
But if we are quoting an excerpt from a single sentence, then we don't normally capitalize.
He insisted we leave "in the morning".
This case is ambiguous because it's a nonsense word, so we don't know if it's supposed to be a complete sentence, an exclamation, or just a fragment. I would have capitalized it also, as it seems like the implication is that it's quoting the entirely of what he said, which would presumably be construed as a full sentence. But it's debatable.