In English, it is grammatically incorrect to have a double negative in a sentence. In a negative sentence (a negative verb) you have to use ´anything´. So as you have ´I canNOT´ you have to use anything. ´I cannot think of anything´.
Anything is also used for questions. Can you think of anything?
I wouldn't say that it's grammatically incorrect. But I would say that the meaning of the sentence gets reversed: "I cannot think of anything" - I have no idea, my mind is blank. "I cannot think of nothing" - My mind works fulltime, I can't stop thinking.
So the second sentence is not a valid translation, but still grammatically correct.
Yes you´re right. wiki doesn´t say anything about it. We should follow the rule for ´some´, ´any´ and ´none,nobody etc) as this is more exact. Any is used in questions and negative sentences. None (nothing, nobody etc) is used for affirmatives. Like you said ´i couldn´t find anything´. you wouldn´t say ´I couldn´t find nothing´.
In theory, in Standard English if two negatives were to be used together they would cancel each other out and become a positive. So if you genuinely mean your sentence to be negative, two negatives should not be used together. This is why English is not a language which accepts using double negatives in the same way as the romance languages for example. Of course standard English is not what most people speak, so you will hear people using such structures, but it sounds unnatural to most and regarded as sub standard English.
I would interpret "I cannot think about nothing" and "I cannot think about anything" as having two different (and almost opposite) meanings. The first means you cannot clear your mind. It could be a response to someone telling you to "relax and don't think about anything". The second sentence means you cannot concentrate. Would someone ever say "I cannot think about nothing" in this way, in Portuguese?
To emeyr, ain't nothing wrong with the word "ain't". It is used by a large section of the English speaking world and is indispensable in the artistic world. Examples are such famous songs as " Ain't nothing but a hound dog"(Elvis Presley), "Ain't no sunshine when she's gone" (Bill Withers), "Ain't Misbehavin" (Broadway musical)," Ain't that a shame" (Fats Domino), and many more. Objection to the word is just a piece of old snobbery that dates to the days of slavery.
There is quite a difference between standard English (as tested by the SAT/TOEFL exams) and the lyrics of some songs. I am not sure the "ain't" is indispensable in all of the artistic world...Perhaps it's regional. As I remember, the suggestion to teach Ebonics in the Oakland School System was greeted with outrage by members of the community. I guess they didn't want their kids using "ain't."