Tahlil böbrekte sorun göstermedi.

Because Turkish adds case endings directly to nouns.
Here, böbrekte = böbrek + -te.

• böbrek = kidney
• -te = in / at / on

So böbrekte means in the kidney.

This is because of consonant harmony in Turkish. The locative suffix has two main forms: -de and -te. After a voiceless consonant such as k, Turkish uses -te.

Since böbrek ends in k, you get böbrekte, not böbrekde.

It most naturally describes sorun. So the sense is a problem in the kidney, not the test in the kidney.

In other words, the structure is understood as: Tahlil [böbrekte sorun] göstermedi
= The test did not show [a problem in the kidney].

Because sorun is an indefinite direct object here. In Turkish, an indefinite object often appears without the accusative ending.

So:

• sorun göstermedi = did not show a problem
• sorunu göstermedi = did not show the problem

The second version would sound like a specific, already-known problem.

Turkish often leaves out bir when English would use a/an. So sorun by itself can already mean a problem in context.

You could also say böbrekte bir sorun göstermedi. That would still be natural, but bir makes the indefiniteness a little more explicit.

Göstermedi breaks down like this:

• göster- = show
• -me- = negation
• -di = past tense

So göstermedi means did not show.

There is no extra ending for he/she/it in the 3rd person singular, so the verb form works with tahlil.

The subject is tahlil. It is the thing that performs the action of showing.

So the roles are:

• tahlil = subject
• böbrekte = locative phrase
• sorun = object
• göstermedi = verb

Because Turkish normally prefers subject–object–verb word order. Putting the verb last is the most neutral and common pattern.

So this sentence follows a very normal Turkish structure: Tahlil + böbrekte sorun + göstermedi

Yes, it is natural. Turkish often uses göstermek with tests, scans, and results, just like English uses show.

So expressions like these are common:

• Tahlil sorun göstermedi.
• MR bir bulgu göstermedi.
• Film kırık göstermedi.

They all mean that a test or image did not show something abnormal.

Because it is not receiving an accusative or possessive ending here. It is simply taking the locative ending -te.

So:

• böbrek = kidney
• böbrekte = in the kidney
• böbreği = the kidney / his-her-its kidney, depending on context

In this sentence, only the location meaning is needed, so böbrekte is the correct form.

The meaning would stay almost the same: The test did not show a problem in the kidney. The version with bir is a little more explicit about a problem, while the version without bir is slightly more compact and also very natural.

So both are possible, but the original sentence is perfectly normal.