Scalpel is correct on saying that both the full and short infinitives are nouns. Yes and infinitive is the noun form of a verb. Like all nouns they take case suffixes.

An infinitive in nominative case is always the full infinitive.
An infinitive in dative case is always the short infinitive.
An infinitive in accusative case is always the short infinitive.
An infinitive in nominative case is 'always' the short infinitive.
An infinitive in locative case is always the full infinitive. *
An infinitive in ablative case is 'always' the full infinitive. **

* The short infinitive is sometimes used here but I don't suggest this.
** In some historical phrases which are very limited in number, the short infinitive still exist with the ablative: "yemeden içmeden kesildi".


Summary:
(no suffix) nominative : -mek > gitmek
(-e,-a case) dative : -me > gitmeye
(-ı,-i,-u,-ü case) accusative : -me > gitmeyi
(-ın,-in,-un,-ün) genitive : -me > gitmenin
(-de,-da case) locative : -mek > gitmekte
(-den,-dan case) ablative case : -mek > gitmekten

Pick any transitive verb and add an infinitive as object.
Example:

sevmek is a transitive verb. It takes -i case. So we say "öğrenmeyi seviyorum", "okumayı seviyorum".

Hoşlanmak is a transitive verb. It takes -den case. So we say "öğrenmekten hoşlanıyorum", "okumaktan hoşlanıyorum".

istemek is a transitive verb. It takes both the accusative case or nominative case. So we say "öğrenmek istiyorum", "okumak istiyorum".

"An infinitive in nominative case is always the full infinitive."
This is correct in any case including noun sentences.

"Türkçe öğrenmek çok kolay."
"Yüzmek çok güzel."

The short infinitive doesn't exist in nominative case except,
1. building permanent nouns: düşÃ¼nme, yüzme, okuma
2. creating noun modifications: yürüme hızı, dönme süresi, gitme zamanı.

Bod,
It is not only istemek but there are other verbs that take an infinitive as an object in nominative case.

Gerekmek is a second one:
"Çok konuşmak gerekmez."
"Çok su içmek gerekiyor."
Olmak is a third one:
"Gitmek olmaz."
"İlk yapacağım şey uyumak olacak."

So I found three verbs (istemek, gerekmek, olmak) so far in this category. Sorry, I don't know any source that includes this kind information. Some information I give in forums I derive on my own.

Scalpel,
I too wrote many times that infinitives are nouns.

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Yes, it is two times negative. There is nothing wrong with this. Your translation is also very good.

Hiçbir şey görmedim : I didn't see nothing.

This is a literal translation. This is the way we speak. There are always differences between languages. You just need to accept them and move on. If you fight with the language you just lose time.

By the way I have heard people saying "Don't shoot nobody" (Eddie Murphy said this in a movie) or "Don't say nothing" so it might be more reasonable than it looks at first glance.

All entries mentioned so far have been processed.

Cyrano's sentences look good. I will add all additions to opening message shortly.

I will make it alphabetical when it becomes too much to follow.

OK. I will add the translations and I will put all entres together and reorganize them according frequency (roughly) when we have at least a few hundred entries. Actually there should be more than 1000 entries so we can choose the more common ones among them.

Let's see how intense the contribution will be from our Turkish members. Actually I would be interested to hear more pattern sentences such as "müsait bir yerde inecek var". These are the funny details of a language.

I can give an example from English on what I mean by pattern sentences. I think, this is a pattern sentence: "Let's get the hell out of here".