Ég get ekki skráð mig inn ef ég man ekki PIN-númerið mitt.

This is a very common learner question.

After geta meaning can / be able to, Icelandic normally uses the sagnbót form of the next verb, not the dictionary infinitive. For many verbs, that form looks like a neuter past participle.

So:

• ég get skráð mig inn
• ég get lesið þetta
• ég get gert þetta

That does not make the sentence past tense. It is just the form Icelandic uses after geta.

Compare this with verbs like vil or ætla, where you use the infinitive instead:

• Ég vil skrá mig inn.
• Ég ætla að skrá mig inn.

So get ... skráð is normal here.

Yes. The expression is skrá sig inn, literally something like register oneself in. In modern usage, it is the normal way to say log in / sign in.

The reflexive pronoun changes with the subject:

• Ég skrái mig inn — I log in
• Þú skráir þig inn — you log in
• Hann/Hún skráir sig inn — he/she logs in

So in your sentence, mig is there because the subject is ég.

Inn is a particle/adverb that belongs with the verb phrase skrá sig inn.

It helps create the meaning log in / sign in. Without inn, skrá usually means something more like register, record, write down.

This is similar to how English often builds meanings with particles:

• log in
• sign in
• check in

Icelandic does this a lot too. Some useful related expressions are:

• skrá sig inn — log in
• skrá sig út — log out / sign out

So it is best to learn skrá sig inn as a whole expression.

In Icelandic, ekki usually comes after the finite verb.

So:

• Ég get ekki ...
• ég man ekki ...

That is the normal position for negation in simple clauses.

A rough pattern is:

• subject + finite verb + ekki + rest

Examples:

• Ég skil ekki. — I do not understand.
• Hún kemur ekki í dag. — She is not coming today.
• Við vitum ekki svarið. — We do not know the answer.

Because the second part is a full subordinate clause introduced by ef (if).

So Icelandic, like English, needs its own subject there:

• Ég get ekki skráð mig inn
• ef ég man ekki PIN-númerið mitt

Literally, this is structured like:

• I cannot log in
• if I do not remember my PIN number

You cannot normally leave out the second ég.

Because muna is the dictionary form, but the present tense is irregular.

The verb is:

• að muna — to remember

But the present singular forms include:

• ég man — I remember
• þú manst — you remember
• hann/hún man — he/she remembers

So ég man ekki means I do not remember.

This is just something you need to learn as an irregular pattern.

In Icelandic, when you mean my specific X, it is very common to use:

• the noun with the definite article + possessive

So:

• bókin mín — my book
• síminn minn — my phone
• PIN-númerið mitt — my PIN number

This is often the most neutral, natural way to say it.

Mitt PIN-númer is possible, but it usually feels more emphatic or contrastive, like my PIN number as opposed to someone else’s.

So PIN-númerið mitt is the expected everyday wording here.

Both are in the accusative here.

• mig is the accusative form of ég
• PIN-númerið mitt is the direct object of man

Why accusative?

• skrá takes a direct object, so the reflexive pronoun appears in the accusative: mig
• muna can also take a direct object, so PIN-númerið mitt is accusative

A useful detail: with neuter nouns like númer, the nominative and accusative singular usually look the same, so you do not see a visible change in númerið.

The hyphen is normal when an abbreviation or foreign letter-name element is attached to an Icelandic noun.

So:

• PIN-númer
• USB-tengi
• TV-stofa

It helps show that the first part is an abbreviation and the second part is the Icelandic noun.

Then the definite article is added to the whole noun:

• PIN-númerið

Yes. A very natural alternative is:

Ef ég man ekki PIN-númerið mitt, get ég ekki skráð mig inn.

Notice the word order in the main clause:

• get ég
• not ég get

That happens because Icelandic is a verb-second language. When the ef clause comes first, it takes the first position, so the finite verb of the main clause comes next.

So both are correct:

• Ég get ekki skráð mig inn ef ég man ekki PIN-númerið mitt.
• Ef ég man ekki PIN-númerið mitt, get ég ekki skráð mig inn.