Breakdown of Ég hef verið á eyðieyjunni síðan skipið brann.
vera
to be
ég
I
á
onto / on / in (static location) / on (a day of the week)
skipið
the ship
Questions & Answers about Ég hef verið á eyðieyjunni síðan skipið brann.
Does síðan need the word að after it?
No. When síðan is used as a temporal conjunction meaning "since" to connect a main clause to a past event, it stands alone. You do not need to add að after it.
Why do we use the simple past tense (brann) after síðan, rather than the present perfect?
Just like in English, síðan points to the specific moment in the past when a situation started. The main clause uses the present perfect (hef verið - have been) for the ongoing state, but the síðan clause uses the simple past (brann - burned) to mark the starting trigger.
Why is eyðieyjunni in the dative case here?
The preposition á (on) governs the dative case when it describes a stationary location ("being on the island"). If you were traveling to the island, á would take the accusative case instead. The -nni suffix is the attached definite article, making this feminine noun definite ("the" desert island).
Brann looks quite different from its infinitive. What is the base verb here?
The infinitive is brenna (to burn). It is a strong verb, meaning it changes its internal vowel in the past tense rather than adding a regular ending (similar to the English sing/sang). The 3rd person singular past tense is brann (it burned).