Ég finn ekki verkfærin í geymslunni, svo ég bið þig að hjálpa mér.

In Icelandic, the negation ekki usually comes after the finite (conjugated) verb in a main clause:

• Ég finn ekki ... = I do not find ... This is the normal V2-style placement: the verb comes early, and ekki follows it (typically before objects/adverbials).

verkfærin is accusative plural definite of verkfæri (tool).

• The verb finna (to find) takes a direct object in the accusative, so verkfærin appears in accusative.
• -in marks definite plural here (the tools, not just tools in general).

geymslunni is dative singular definite of geymsla (storage room). With í, Icelandic distinguishes:

• Location (static) → dative: í geymslunni = in the storage room (where something is)
• Movement (direction) → accusative: í geymsluna = into the storage room (motion toward)

The ending -unni is the definite dative singular form.

svo here works like so / therefore, linking two clauses: 1) Ég finn ekki verkfærin í geymslunni, 2) svo ég bið þig að hjálpa mér.

It introduces a consequence clause. In writing, it’s common to use a comma before it when it clearly separates two full clauses.

Icelandic typically states the subject in each clause, especially in careful/neutral style:

• ..., svo ég bið ... is fully explicit.

In some contexts (especially informal speech), you might hear ellipsis, but repeating ég is normal and clear, and it avoids ambiguity.

þig is the accusative form of þú (you, singular). The verb biðja (to ask/request) commonly takes:

• the person being asked in the accusative: biðja þig = ask you So:
• þú = nominative (subject)
• þig = accusative (object)
• þér = dative (used with verbs/prepositions that govern dative)

Here, you are the direct object of bið.

After biðja (and many other verbs), Icelandic often uses an infinitive clause introduced by að:

• biðja [someone] að [do something] So að hjálpa is an infinitive meaning to help, and að is the marker introducing that infinitive clause.

Both patterns are used, but many speakers consider biðja einhvern um að ... especially common/idiomatic:

• Ég bið þig um að hjálpa mér.

Your sentence Ég bið þig að hjálpa mér is also heard and understood, but if you want the safest, most widely accepted phrasing, add um.

Because hjálpa governs the dative for the person receiving help:

• hjálpa mér (dative) = help me Not mig (accusative).

So the pronoun changes:

• ég (nom) → mig (acc) → mér (dat)

Here, mér is required by hjálpa.

Yes:

• finn = 1st person singular present of finna (to find)
• bið = 1st person singular present of biðja (to ask/request)

Both agree with Ég (I). Icelandic verbs conjugate for person/number, so the ending (or stem change) signals I even though the subject is still usually written.