Learn German: Ich hätte das Trinkwasser in der Notlage abgekocht. - I would have boiled the drinking water in the emergency situation.

Hätte combined with the past participle abgekocht forms the past tense of the subjunctive II (Konjunktiv II). It translates to "would have boiled." If you used the helper verb würde plus the infinitive (würde abkochen), it would mean "would boil" in the present or future, rather than describing a hypothetical situation that didn't happen in the past.

Why is the prepositional phrase in der Notlage in the dative case rather than accusative?

The preposition in is a two-way preposition. Even though an emergency is abstract and not a physical room, it describes a static state or condition answering the question of where or in what situation something happens. Because there is no direction of movement into a new state, it takes the dative case, changing the feminine article die to der.

How could we use the genitive preposition mangels to explain why the water had to be boiled in this sentence?

You can insert mangels (for lack of) to express why the boiling was necessary. For example, you could say Ich hätte das Trinkwasser in der Notlage mangels sauberer Alternativen abgekocht (I would have boiled the drinking water in the emergency for lack of clean alternatives). Because Alternativen is plural and has no article here, the adjective sauberer takes the genitive plural ending -er.

How could we add to this sentence to express the purpose of boiling the water?