He pointed out that you used the wrong particle. You say “nihongo ga hanasenai” but “nihongo wo hanasanai”.
This is the adverbial suffix -e; not really a part of a declension, just roughly equivalent to the English suffix -ly. However–like in English–note that not all adjectives can be made into adverbs this way in Latin.
“I do not speak Latin” is Latine non loquor. Without native speakers, classicists often appeal to the remaining literature, and we have a pretty clear example from Livy (XL.43), where between the 2nd and 3rd Macedonian wars he notes that: Cumanis eo anno petentibus permissum, ut publice Latine loquerentur et praeconibus Latine vendendi ius esset. - “In that same year the citizens of Cumae sought the right to speak Latin in matters of law and commerce.”
Your Turkish sentence needs correction.
Türkçe bilmiyorum.
Literally, ‘I don’t know Turkish’ is how you’d say it. But the negative first person present tense of the verb “to speak” would be konuşmuyorum.
Bonus languages
Modern Standard Arabic:
لا أعرف اللغة العربية
Lā a‘rifu al-lughah al-‘Arabīyah. (literally, “I don’t know” again instead of “I don’t speak”)
Egyptian Arabic:
أنا مش بتكلم عربي
Ana mish batkallem ‘Arabī.
Hindi:
मैं हिन्दी बोलता नहीं हूँ.
Maiṁ Hindī boltā nahīṁ hūṁ. (male speaker)
मैं हिन्दी बोलती नहीं हूँ.
Maiṁ Hindī boltī nahīṁ hūṁ. (female speaker)
Indonesian and Malay:
Saya tidak bercakap Bahasa Indonesia.
Saya tidak bercakap Bahasa Melayu.
Italian:
Non parlo italiano.
Tamil:
நான் தமிழ் பேச தெரியாது.
Nān Tamil pēca teriyātu.
Telugu:
నేను తెలుగు మాట్లాడటం లేదు.
Nēnu Telugu māṭlāḍaṭaṁ lēdu.
Uzbek:
O’zbekcha gapirmayman.
Bonus language:
(aš) nekalbu lietuviškai - I don’t speak Lithuanian
In Russian, you can also use “Я не понима́ю по-русски” - Ya nee ponimayu po-russki - which means “I don’t understand Russian”.
Nemluvím česky - I don’t speak Czech.
No parlo català - I don’t speak Catalan.
Jeg taler ikke dansk - I don’t speak Danish.
Mi ne parolas Esperanton - I don’t speak Esperanto.
I don’t speak Breton:
Brezhoneg ne gomzan ket or Brezhoneg ne ran ket.
(brezonek negomzan ket / brezonek neran ket)
I don’t speak Welsh:
Dydw i ddim yn siarad Cymraeg / Dw i ddim yn siarad Cymraeg
(dud-oo ee thim un sharad kum-rye·gg / doo ee thim un sharad kum-rye·gg,
thim with th as in them and rye·gg meant to rhyme with tig in tiger)
Sindarin: Ú-bedin edhellen
Pronunciation: 'uˑ.bɛ.din ɛ.'ðɛl̡.lɛn
English: I don’t speak Elvish
No one has done Klingon yet? I’m shocked!
I would say
“No hablo español”
Literally “Don’t speak spanish”
In an interesting twist of the language, you don’t need to put the personal pronoun, because that information is stored in the conjugation of the verb.
Verb: hablar
“Yo hablo”
It’s a way of knowing if the speaker is not native in the language (especially english) because they’ll use the pronoun “Yo” (which means “I”, by the way)
And about the german, it is correct to say “Ich kann nicht Deutsch”, it’s like saying “I know no german”.
No. Literally “I don’t speak Spanish”. There is no way to treat hablo as not incorporating “I”.
Well… yes, but I meant you don’t need to write a separate word for the pronoun “I”.
If this were a linguistics class, we’d write it:
no habl-o español
**not speak**-PR.1SG **Spanish**
With Russian, I also wanted to find out how to say “You clumsy fool!” and “Frank [as in “Sinatra”], what are you doing here?” Thanks. 
While I agree that ‘nihongo ga hanasanai’ is in the wrong, as you may very well know there are instances of wo being used instead of ga with the potential form of the verb. I personally am not aware of the difference in nuance between ‘nihongo ga hanasenai’ (the proper way to say it) and ‘nihongo wo hanasenai’. An example of the latter usage is found here, in the first paragraph.. If I was speaking this phrase out loud to describe somebody, I would probably leave the particle out altogether. For example, ‘kare sa, nihongo hanasenai yo.’ On further thought, I would probably use ‘wakaranai’ instead as well.
Getting back to grammar, IIRC, I believe I have also even heard ‘nantoka wo wakaru’ before.. I could swear some old Japanese people have asked me ‘nihongo wo wakarimasu ka?’ a few times… But now I’ve gotten really off track!
This is wrong, too. It’s nie mówię po polsku
If you want to know more than you possibly thought possible to know about this question, I direct you to this 17-page paper:
可能動詞の助詞に関する一考察 (big pdf!)
One of the factor the author highlights is the strength of the speaker’s intent. For instance, if you search for “英語を話せる”, you will find that a very large proportion of the hits are for the phrases like “英語を話せるようになる” (literally, “becoming so that English can be spoken”). The same phrase with “ga” used instead is also common, but by putting “English” or “Japanese” as an object rather than a subject, the speaker is putting the subject in a more assertive position.
If you look at actual usage of “eigo wo hanasenai”, you will find that in almost every case, the subject is important. Examples:
Nihon-jin ga eigo wo hanasenai riyuu (The reason why Japanese can’t speak English.)
Anata ga eigo wo hanasenai nara (Should you not be able to speak English)
Eigo wo hanasenai joushi ga iru (I have a supervisor who can’t speak English)
The first sentence above can’t be written with ga, because it would break the clause modifying riyuu.
To use ga in the second sentence, you would need to make anata (you) the theme: “Anata wa eigo ga hanasenai nara”. However, if you do this, you are strongly insinuating that other people can speak English. The original sentence is neutral and doesn’t single out the subject.
The last sentence is the only one where ga and wo can be used interchangeably. This is because the person in question is mentioned outside of the verbal clause.
Yeah, but like Matt and John say, it’s because hablo means “I speak”, it doesn’t mean “speak”.
Not only is having too many explicit subjects a way to tell that a text has been written/translated into Spanish by someone who wasn’t thinking in Spanish, but the opposite is a common mistake of Hispanics when speaking languages which require explicit subjects. We have a real big problem when speaking in the first person singular in English, because in Spanish expliciting yo more than once per conversation sounds horribly self-centered and impolite.
I was going to but then I realized that “I don’t speak Klingon” 
I realize that the members of this group are of an international nature, but why learn a long list of phrases. Any good red-blooded American knows that if you just say it in English but very slowly and loudly that anybody can understand what you are saying. :rolleyes: