Το κλειδί δεν είναι εδώ, και χωρίς αυτό δεν ανοίγει η πόρτα.

Κλειδί means key, and it is a neuter noun in Greek.
That is why it takes the neuter singular article το:

• το κλειδί = the key

In Greek, every noun has a grammatical gender: masculine, feminine, or neuter.
The article has to match the noun’s gender, number, and case.

Here:

• το = neuter singular the
• κλειδί = key

So το κλειδί is simply the key.

Because Greek usually puts δεν directly before the verb it negates.

In this sentence there are two verbs:

• δεν είναι εδώ = is not here
• δεν ανοίγει η πόρτα = the door does not open

So each negative verb gets its own δεν.

This is very normal in Greek. You do not usually use one negative word for the whole sentence if there are two separate verb phrases.

Είναι εδώ means is here or is present here.
So Το κλειδί δεν είναι εδώ means The key is not here.

If you said δεν υπάρχει εδώ, that would mean something more like:

• it does not exist here
• it is not to be found here

That can work in some contexts, but δεν είναι εδώ is the natural everyday way to say that an object is not in this place.

Χωρίς means without.

In Modern Greek, χωρίς is normally followed by the accusative case.

So:

• χωρίς αυτό = without it

Here αυτό refers back to το κλειδί.

Some more examples:

• χωρίς νερό = without water
• χωρίς το παιδί = without the child
• χωρίς εμένα = without me

Because αυτό is the pronoun it, and it must match κλειδί, which is neuter singular.

Here are the relevant forms:

• αυτός = he / this one / that one (masculine)
• αυτή = she / this one / that one (feminine)
• αυτό = it / this one / that one (neuter)

Since κλειδί is neuter, the correct pronoun is αυτό:

• χωρίς αυτό = without it

You would not use το by itself here to mean it.
And αυτόν is masculine accusative, so it would not agree with κλειδί.

Here it means the door does not open or more naturally the door won’t open.

That is because η πόρτα is the subject:

• η πόρτα = the door

If the sentence meant someone does not open the door, then the door would be the object, so you would normally expect:

• δεν ανοίγει την πόρτα = he/she is not opening the door

Notice the difference:

• η πόρτα = nominative case, subject
• την πόρτα = accusative case, object

So δεν ανοίγει η πόρτα means the door itself is not opening.

Greek word order is more flexible than English word order.

Both of these are possible:

• Η πόρτα δεν ανοίγει.
• Δεν ανοίγει η πόρτα.

The second version can sound a bit more natural in this context, especially after the explanation χωρίς αυτό. It puts focus on the result:

• without it, the door doesn’t open

So the word order helps the sentence flow, but the meaning is still clear because the article η shows that πόρτα is the subject.

Greek uses the definite article much more regularly than English.

So when talking about a specific key and a specific door, Greek naturally says:

• το κλειδί = the key
• η πόρτα = the door

Leaving the article out would usually sound unnatural here.

In this sentence, αυτό functions as a pronoun meaning it.

Greek αυτός / αυτή / αυτό can mean:

• he / she / it
• this
• sometimes that, depending on context

Here, because it refers back to το κλειδί, the natural translation is it:

• χωρίς αυτό = without it

So even though the form is the same as the demonstrative this, the function here is pronominal.

Yes.
Και means and.

It links the two parts of the sentence:

• Το κλειδί δεν είναι εδώ = The key is not here
• και χωρίς αυτό δεν ανοίγει η πόρτα = and without it the door does not open

So the full sentence is built from two connected ideas.

Yes, very often in context it can.

Greek present tense can sometimes sound more general or more immediate than the English simple present. In a real-life situation, δεν ανοίγει η πόρτα often means:

• the door won’t open
• the door isn’t opening

So although the literal structure is the door does not open, the natural English meaning may vary depending on context.

Greek allows some variation, for example:

• Το κλειδί δεν είναι εδώ και η πόρτα δεν ανοίγει χωρίς αυτό.
• Χωρίς αυτό, η πόρτα δεν ανοίγει.
• Η πόρτα δεν ανοίγει χωρίς το κλειδί.

These all express very similar meanings.

The original sentence:

• Το κλειδί δεν είναι εδώ, και χωρίς αυτό δεν ανοίγει η πόρτα.

has a nice natural flow: first it states the problem, then it gives the consequence.