Ef við hefðum athugað rennilásinn fyrr, hefði ég ekki þurft að halda jakkanum saman með hendinni alla leið í vinnuna.

It is a past unreal conditional sentence: it talks about something that did not happen in the past and the consequence that would also not have happened.

Structure here:

• Ef við hefðum athugað rennilásinn fyrr = If we had checked the zipper earlier
• hefði ég ekki þurft ... = I would not have had to ...

So the speaker is describing a past situation contrary to fact.

In this kind of counterfactual past sentence, Icelandic commonly uses:

• past subjunctive of hafa
• plus a past participle

So:

• hefðum athugað = had checked
• hefði þurft = would have had to

English uses different-looking patterns in the two clauses (had checked / would have had to), but Icelandic often uses very similar perfect-style forms in both clauses.

They agree with the subject:

• við hefðum = we had
• ég hefði = I would have / had

So the ending changes because the subject changes from við to ég.

That is because of the verb-second rule in Icelandic.

When the sentence begins with the if-clause:

• Ef við hefðum athugað rennilásinn fyrr, ...

the finite verb of the main clause comes first, before the subject:

• hefði ég ekki þurft

If the second clause stood alone, you would normally say:

• Ég hefði ekki þurft ...

So this inversion is completely normal Icelandic word order.

They are past participles:

• athugað = past participle of athuga
• þurft = past participle of þurfa

After hafa, Icelandic uses the past participle to build perfect-style forms.

A useful point for learners: in these hafa + past participle constructions, the participle usually stays in its default form and does not change for gender or number.

Because it means the zipper, not just a zipper.

• rennilás = zipper
• rennilásinn = the zipper

Icelandic usually puts the definite article onto the end of the noun instead of using a separate word like English the.

Also, here rennilásinn is the direct object of athugað, so it is in the accusative singular definite form.

Fyrr means earlier.

That fits the logic of the sentence: the idea is not just early in general, but earlier than we actually did.

So:

• fyrr = earlier
• snemma = early

In this sentence, fyrr is the natural choice because the speaker is comparing reality with a better earlier time.

Because þurfa normally takes að + infinitive when it means need to / have to.

So:

• þurfa að gera eitthvað = to need to do something

Here:

• þurft að halda = had to hold / needed to hold

That is a very common Icelandic pattern.

Because halda in this meaning governs the dative.

Here halda means something like hold, keep, or keep together, and the thing being held is in the dative:

• halda jakkanum saman = hold the jacket together

So:

• jakki = jacket
• jakkanum = the jacket, dative singular definite

This is something you often just have to learn with the verb: certain Icelandic verbs require a particular case.

Saman means together.

Without it, halda jakkanum would just mean hold the jacket.
With saman, the meaning becomes more specific:

• halda jakkanum saman = hold the jacket together

That strongly suggests the jacket is not properly closed, probably because the zipper is broken or open.

Because með takes the dative.

So:

• hönd = hand
• hendinni = the hand, dative singular definite

That is why you get:

• með hendinni = with the hand

This phrase expresses the instrument used to do something: the speaker used their hand to hold the jacket together.

This is a very common Icelandic habit, especially with body parts.

When it is obvious whose body part is meant, Icelandic often uses:

• the definite noun
• without an explicit possessive

So:

• með hendinni literally = with the hand
• but naturally in English = with my hand

You certainly can add a possessive in Icelandic if needed for emphasis or clarity, but very often it is unnecessary.

Alla leið means all the way.

So:

• alla leið í vinnuna = all the way to work

It expresses the full distance or duration of the trip. The idea is that the speaker had to keep holding the jacket together for the entire journey.

Because í can take either:

• accusative for motion toward / into
• dative for location in

Here the meaning is directional:

• alla leið í vinnuna = all the way to work

So Icelandic uses the accusative:

• vinnuna

Compare:

• ég er í vinnunni = I am at work / in the workplace
• ég fer í vinnuna = I go to work

Literally, yes, it is based on vinna = work, with the definite form vinnuna. But as a phrase, fara í vinnuna or alla leið í vinnuna is just the normal Icelandic way to say go to work or all the way to work.

So it should be learned as a natural expression, not translated word-for-word too rigidly.

Yes. You could also say:

• Ég hefði ekki þurft að halda jakkanum saman með hendinni alla leið í vinnuna ef við hefðum athugað rennilásinn fyrr.

That means the same thing.

The difference is mostly one of focus and style:

• starting with Ef ... highlights the condition first
• starting with Ég hefði ... highlights the consequence first