Ég kemst ekki inn, því hurðin er föst.

Because the verb here is komast, not koma.

• koma = to come
• komast = to get somewhere / manage to get somewhere / be able to make one’s way

So:

• Ég kem = I come
• Ég kemst = I get there / I manage to get there

In Ég kemst ekki inn, the speaker is not just saying I don’t come in, but rather I can’t get in.

Also, kemst is the 1st person singular present form of komast.

Here komast means something like:

• to get in
• to be able to get in
• to make one’s way in

It often implies that there is some obstacle, difficulty, or limitation.

So Ég kemst ekki inn suggests:

• the speaker is trying to enter,
• but something is preventing it.

That makes it a very natural choice before því hurðin er föst.

In Icelandic, ekki usually comes after the finite verb.

So:

• Ég kemst ekki inn = I can’t get in

Compare:

• Ég sé ekki = I do not see
• Hann er ekki hér = He is not here

This is different from English, where we often use do not or place not differently.

A useful beginner pattern is:

• Subject + finite verb + ekki + rest

So here:

• Ég = subject
• kemst = finite verb
• ekki = not
• inn = in / inside

Inn means in or inside, especially with movement into a place.

In this sentence, it works like a directional adverb:

• komast inn = get in / get inside

This is different from just describing location.

For example:

• Ég er inni = I am inside
• Ég fer inn = I go in
• Ég kemst inn = I get in

So inn is about movement into somewhere, not just being there.

Því can mean because in Icelandic, especially in written or slightly more formal style.

So:

• Ég kemst ekki inn, því hurðin er föst. = I can’t get in, because the door is stuck.

Another very common way to say because is:

• af því að

For example:

• Ég kemst ekki inn af því að hurðin er föst.

Both are correct.
Því is just shorter and often feels a bit more written or formal.

Because því introduces the reason clause: because the door is stuck.

So the sentence is divided into:

1. Ég kemst ekki inn
2. því hurðin er föst

In Icelandic, it is very common to separate clauses like this with a comma.

So the comma helps show:

• main statement: I can’t get in
• reason: because the door is stuck

Because hurðin means the door, while hurð means a door / door.

Icelandic usually adds the definite article (the) to the end of the noun:

• hurð = door
• hurðin = the door

Here the speaker means a specific door, so hurðin is needed.

This is a very important Icelandic pattern:

• bíll = car
• bíllinn = the car
• kona = woman
• konan = the woman

So:

• hurðin er föst = the door is stuck

Because the adjective must agree with hurðin.

• hurð is a feminine noun
• hurðin is singular
• it is the subject of the clause, so it is in the nominative

The adjective fastur (stuck, fixed) changes form to match the noun:

• fastur = masculine
• föst = feminine
• fast = neuter

So:

• hurðin er föst = the door is stuck

This kind of adjective agreement is very important in Icelandic.

It can mean several related things depending on context, including:

• stuck
• jammed
• fixed
• sometimes fastened

In this sentence, stuck or jammed is the most natural meaning.

So hurðin er föst suggests:

• the door will not open properly,
• not necessarily that it is locked with a key.

If the idea were specifically locked, Icelandic might use a different expression, depending on context.

Because after því meaning because, Icelandic often keeps normal clause order here:

• hurðin = subject
• er = verb
• föst = adjective/complement

So:

• því hurðin er föst = because the door is stuck

For a learner, it is helpful to read this as a normal mini-sentence after the conjunction:

• the door is stuck

Yes, you could say that, but it is not exactly the same.

• Ég kemst ekki inn = I can’t get in / I’m unable to get in
• Ég get ekki farið inn = I can’t go in

The second version focuses more on being unable to go in, while komast inn is especially natural when something blocks access physically.

Because the next clause says the door is stuck, Ég kemst ekki inn is the most idiomatic choice.

Yes, very much so. It sounds natural and idiomatic.

Icelandic often uses komast in situations where English uses expressions like:

• get in
• get out
• get there
• manage to reach
• be able to make it

Examples:

• Ég kemst ekki út. = I can’t get out.
• Við komumst heim. = We got home.
• Hann komst ekki til vinnu. = He couldn’t get to work.

So this sentence is a very useful everyday pattern to learn.