Við fundum lykilinn á endanum.

• Við = we
• fundum = found
  This is the 1st person plural past tense of finna (to find).
• lykilinn = the key
  This is lykill (key) with the definite article attached, and in the form required by the verb.
• á endanum = in the end / eventually / at the end
  This is a very common Icelandic expression.

So the structure is basically:

Við + fundum + lykilinn + á endanum
We + found + the key + in the end

Because fundum is the past tense, while finnum is present tense.

The verb is finna (to find), and it changes its stem in the past tense:

• ég finn = I find
• við finnum = we find
• ég fann = I found
• við fundum = we found

So:

• Við finnum lykilinn = We find / are finding the key
• Við fundum lykilinn = We found the key

This kind of vowel change is common in Icelandic strong verbs.

Because lykill is the basic dictionary form, but after the verb finna, the object has to be in the accusative case.

Here is the noun:

• lykill = key (nominative singular, indefinite)
• lykil = accusative singular, indefinite
• lykilinn = accusative singular, definite = the key

Since fundum is acting on a direct object, Icelandic uses the accusative:

• Við fundum lykil = We found a key
• Við fundum lykilinn = We found the key

So -inn here is the attached word for the.

In Icelandic, the definite article is usually attached to the end of the noun instead of being a separate word like English the.

So:

• lykill = a key / key
• lykillinn would not be the correct form here
• lykilinn = the key in the accusative singular

The important thing is that both the case ending and the definite article are built into the word.

That is why lykilinn looks longer than the dictionary form lykill.

Á endanum usually means in the end, eventually, or finally.

It is a very common idiomatic expression. In this sentence:

• Við fundum lykilinn á endanum = We found the key in the end / eventually

Depending on context, it can sometimes also feel close to at the end, but very often learners should understand it as the idiomatic in the end rather than a literal physical location.

Because the expression uses a specific case form of endi (end).

The noun endi here appears as:

• endi = nominative singular
• enda = accusative singular
• enda = genitive singular
• enda = dative singular indefinite in some paradigms?
  But in this fixed phrase you most often meet the definite dative singular:
• endanum = the end in the dative

After á, Icelandic can use different cases depending on meaning. In many expressions involving location or a fixed idiom, á takes the dative, and that is what happens here:

• á endanum = literally something like at/in the end

For a learner, the safest approach is to memorize á endanum as a complete expression meaning in the end.

Yes, absolutely.

Even though you can analyze the grammar, á endanum is best learned as a set phrase meaning:

• in the end
• eventually
• finally

This is useful because many Icelandic prepositional expressions do not map neatly onto English word-for-word.

So instead of thinking:

• á = on
• endanum = the end

it is often better to learn:

• á endanum = in the end

Usually Icelandic does include the subject pronoun unless the context makes it very obvious or the sentence structure is doing something special.

So Við fundum lykilinn á endanum is the normal straightforward way to say We found the key in the end.

That is different from some languages where the verb ending alone often lets you omit the pronoun. Icelandic verb endings do give information, but subject pronouns are still commonly used.

Yes. Icelandic word order is fairly flexible, though not random.

The neutral order here is:

• Við fundum lykilinn á endanum.

But you might also see:

• Á endanum fundum við lykilinn.

That version puts more emphasis on in the end. Notice that when another element comes first, the verb often stays in the second position:

• Á endanum
  • fundum
    • við
      • lykilinn

This is a classic Icelandic and Germanic pattern called verb-second word order.

A rough guide is:

Við fundum lykilinn á endanum

Approximate pronunciation: vith FÜN-dum LIH-ki-lin au EN-da-num

A few helpful notes:

• ð in Við is like the th in this
• u in fundum is not like English oo; it is more rounded and central
• ll in Icelandic can have a special pronunciation depending on the word, but in lykill / lykilinn learners often first focus on recognizing the form before mastering every sound detail
• the stress in Icelandic is usually on the first syllable of each word

If you want, the safest beginner strategy is to learn the rhythm: VIÐ fundum LYKilinn Á endanum

The dictionary forms are:

• við = we
• finna = to find
• lykill = key
• endi = end

In the sentence, they appear in changed forms because Icelandic grammar marks:

• person/number/tense on the verb: fundum
• case/definiteness on nouns: lykilinn
• case after prepositions: endanum

So when looking words up, you would search for:

• fundum → finna
• lykilinn → lykill
• endanum → endi