Anahtarı bulamayınca kapıyı açamadım.

Because anahtar is the direct object of bulmak and it is specific/definite here: the key.

In Turkish, a specific direct object usually takes the accusative ending.

• anahtar = a key / key
• anahtarı = the key

So:

• anahtar bulmak = to find a key / find keys
• anahtarı bulmak = to find the key

Here the speaker means a particular key, so anahtarı is the natural form.

Kapıyı is also a specific direct object, so it takes the accusative ending too.

The noun is kapı = door. Because kapı ends in a vowel, Turkish inserts a buffer consonant y before the accusative ending:

• kapı + ı would be awkward
• so Turkish says kapı + yı = kapıyı

So:

• kapı açmak = to open a door / open doors
• kapıyı açmak = to open the door

The y does not add meaning; it is just there to connect the noun and the suffix smoothly.

Bulamayınca means something like when [someone] couldn’t find or since [someone] couldn’t find.

It can be broken down like this:

• bul- = find
• -ama- = not be able to
• -yınca / -ınca = when / since / once

So:

• bulamayınca = when one couldn’t find / since one couldn’t find

In this sentence, it connects the two actions:

• first: not finding the key
• second: not being able to open the door

A natural English link here is often because: Because I couldn’t find the key, I couldn’t open the door.

Açamadım means I couldn’t open.

It breaks down like this:

• aç- = open
• -ama- = not be able to
• -dı = past tense
• -m = I

So:

• açamadım = I couldn’t open / I was unable to open

This is an important pattern in Turkish. Forms like -A-ma- often express inability, not just simple negation.

This is a very important difference.

• açmadım = I didn’t open
• açamadım = I couldn’t open

So:

• açmadım is simple negation. Maybe I chose not to open it, or I simply didn’t do it.
• açamadım shows inability. I tried, or the situation prevented me.

In the same way:

• bulmadım = I didn’t find
• bulamadım = I couldn’t find

Your sentence uses açamadım, so the idea is not just that the speaker failed to open the door as a fact, but that opening it was not possible because the key was missing.

Because Turkish often drops subject pronouns when the verb ending already shows who the subject is.

In açamadım, the ending -m tells us the subject is I.

So Turkish does not need ben unless the speaker wants emphasis or contrast.

• açamadım = I couldn’t open
• ben açamadım = I couldn’t open it

The second version sounds more emphatic, like I couldn’t open it.

The same idea applies to the first part too. Bulamayınca does not state the subject explicitly, but in this sentence it is naturally understood to be the same person as in the main clause: I.

It can suggest either one, depending on context.

-ınca / -ince often means:

• when
• once
• since
• sometimes effectively because

In this sentence, both ideas fit:

• When I couldn’t find the key, I couldn’t open the door
• Because I couldn’t find the key, I couldn’t open the door

But the most natural understanding here is usually because. Not finding the key is the reason the door could not be opened.

So -ınca often links two events with a time relationship, and that time relationship can also imply cause.

By default, in a sentence like this, the subject of the -ınca clause is usually understood from the main clause if no other subject is given.

So in:

• Anahtarı bulamayınca kapıyı açamadım

the natural reading is:

• When I couldn’t find the key, I couldn’t open the door

If you wanted a different subject in the first part, you would normally say it explicitly:

• Ali anahtarı bulamayınca kapıyı açamadım.
• When Ali couldn’t find the key, I couldn’t open the door.

So without another subject being named, learners should normally assume the same subject continues.

Turkish word order is much more flexible than English, but the normal neutral pattern is that the verb comes at the end.

So the sentence is organized like this:

• Anahtarı bulamayınca = when/because I couldn’t find the key
• kapıyı açamadım = I couldn’t open the door

A more literal order would be something like:

• The key not being able to find when, the door I couldn’t open

That sounds strange in English, but it is normal in Turkish.

A few key points:

• subordinate clauses often come before the main clause
• objects often come before the verb
• the main verb usually comes last

So this sentence has very natural Turkish word order.

Yes. Turkish allows other ways to express the same idea, though the original sentence is very natural.

For example:

• Anahtarı bulamadığım için kapıyı açamadım.
  = Because I couldn’t find the key, I couldn’t open the door.

This version uses -dığı için, which is a very direct because structure.

The original:

• Anahtarı bulamayınca kapıyı açamadım

is slightly more compact and can feel like when/since I couldn’t find the key.

So the original sentence is correct and natural; it is just one of several ways Turkish can express this meaning.