Translation:Today I do not have any energy because I did not sleep at all last night.
Building on what Super_Nerd said, in the first clause, 'hiç" is an adjective (made evident by it modifying a noun) and in the second clause it is an adverb (because it is modifying a verb). This has pretty big implications on how it can be translated into English :)
That being said, in some but not all dialects of English, "I didn't sleep any last night" is perfectly fine (I actually prefer to say this, but I am known to speak a lovely variety of Appalachian English that turns a lot of heads in Boston).
Hmm. I find both the explanations here odd. First, in English we would make no differentiation between personal energy and oil energy in choosing whether to say "any" or "at all." If I am translating this sentence into English, shouldn't I observe English rules in the translation? And second, I can't see it makes any difference whether "hiç" is an adjective or an adverb here. "I have no energy at all" equals "I don't have any energy." They state the same idea, but one does it with a positive verb and one does it with a negative verb, which switches you between "no ... at all" and "any." And "hiç" in the dictionary is defined as either one of those.
"Bugün hiç enerjim yok çünkü dün gece hiç uyumadım." Translation: Today I do not have any energy because I did not sleep at all last night.
Today I do not have any energy because last night I did not sleep at all.
Correct other English answer & word order accepted by Duo.