SIM-kortet ligger derinde.

Because Danish usually treats this kind of expression as a compound noun. The main noun is kort, and SIM is added in front to specify what kind of card it is.

So:

• et kort = a card
• et SIM-kort = a SIM card
• SIM-kortet = the SIM card

The hyphen is common when the first part is an abbreviation like SIM.

That ending is the Danish way of saying the.

In English, you say the card with a separate word. In Danish, the definite article is usually attached to the end of the noun:

• et kort = a card
• kortet = the card

Since SIM-kort is based on et kort, its definite form becomes SIM-kortet.

Because Danish normally puts definiteness on the noun itself instead of using a separate word.

So English:

• the SIM card

Danish:

• SIM-kortet

A separate word like det is usually added only in certain cases, especially when there is an adjective:

• det lille SIM-kort = the small SIM card

But in your sentence, there is no adjective, so SIM-kortet by itself is enough.

Danish often uses position verbs where English would simply use is.

Here, ligger comes from at ligge, which means to lie or to be lying. It is commonly used for things that are resting somewhere, especially if they are thought of as lying flat or simply being located somewhere as an object.

So:

• SIM-kortet ligger derinde sounds natural in Danish.
• SIM-kortet er derinde is understandable, but less specific and often less idiomatic.

Danish uses several verbs like this:

• ligge = lie / be lying
• stå = stand / be standing
• sidde = sit / be situated or attached

English often just uses be, but Danish prefers these more descriptive verbs.

Derinde means in there or inside there.

It is made up of:

• der = there
• inde = inside, in

Together, derinde points to a specific place that is already understood from the context.

So it is more specific than just inde:

• inde = inside
• derinde = in there

Because in Danish, combinations like this are commonly written as a single adverb.

So derinde is a fixed form meaning in there. Danish has several similar words:

• derude = out there
• deroppe = up there
• dernede = down there

English writes these as two words, but Danish often writes them as one.

This is actually the normal word order for a simple main clause:

• SIM-kortet = subject
• ligger = verb
• derinde = adverb of place

So the pattern is:

subject + verb + place

However, Danish main clauses follow the verb-second rule, which means the finite verb usually stays in the second position. That becomes easier to notice if something else comes first:

• Derinde ligger SIM-kortet.

That version is also correct, but now derinde is in first position, so the verb ligger still has to stay second.

Yes. That is a perfectly correct sentence.

The difference is mainly focus:

• SIM-kortet ligger derinde = neutral statement about where the SIM card is
• Derinde ligger SIM-kortet = more emphasis on the location, roughly In there is where the SIM card is

So both are grammatical, but they highlight different parts of the sentence.

Ligger is the present tense of at ligge.

Some useful forms are:

• at ligge = to lie
• ligger = lies / is lying
• lå = lay / was lying
• har ligget = has lain / has been lying

So SIM-kortet ligger derinde is in the present tense.

It is neuter, because the main noun is kort, and kort is a neuter noun:

• et kort

In Danish compounds, the last part usually determines the grammatical gender. So:

• et kort
• et SIM-kort
• SIM-kortet

That is why the definite ending is -et, not -en.