Learn Turkish: Ahşap masayı çekiyordum; sanki elime büyük bir kıymık battı. - I was pulling the wooden table; it was as if a large splinter pierced my hand.

The tam... -(y)AcAktI ki structure means you were just about to do something, but got interrupted before you could start. In this sentence, the action of pulling the table was already actively happening. Therefore, the past continuous (-(I)yordu) is the correct choice for an ongoing background action that gets interrupted by a sudden event in the simple past (battı).

Why do we use the dative case in elime (to/into my hand) rather than the locative case elimde (in my hand)?

The verb batmak generally means to sink. When talking about splinters, thorns, or needles, it describes the motion of the object piercing into the skin. Because it describes movement toward a destination, Turkish requires the dative case (elime).

Could I translate 'pierced my hand' as elimi battı using the accusative case for a direct object?

No, because batmak is an intransitive verb in Turkish, meaning it cannot take a direct object. While English says it pierced the hand, Turkish frames it as the splinter sinking into the hand, which is why it must take the dative case (elime) instead of the accusative (elimi).

Why is the word order büyük bir kıymık instead of bir büyük kıymık?