Learn Hardcore Polish: Głośnik w tramwaju jest zepsuty, dlatego kurier nie usłyszał naszej decyzji. - The speaker on the tram is broken, therefore the courier did not hear our decision.

In Polish, to describe a subject’s state in the present you normally need a form of the verb być (“to be”). Here jest is the third person singular present tense (“is”). So Głośnik jest zepsuty literally means “The speaker is broken.”
You can’t omit jest in standard Polish (unlike in headlines or very casual speech).
If you want to focus on the action of breaking rather than the resulting state, you use the reflexive perfective verb zepsuć się (“to break down”):
• Głośnik zepsuł się – “The speaker broke down.”

Why is w tramwaju in the locative case, and how do we form it?

The preposition w (“in”) requires the locative case when it indicates location. The base noun is tramwaj (tram), and its locative singular form is tramwaju. Thus w tramwaju = “in the tram.”

What part of speech is zepsuty and how is it formed?

Zepsuty is a past passive participle that functions as an adjective meaning “broken.” It’s derived from the perfective verb zepsuć (“to break/spoil”) and agrees with the noun’s gender, number, and case. For a masculine singular noun you get zepsuty; feminine singular would be zepsuta, neuter zepsute, and so on.

How does dlatego function in this sentence, and how does it differ from ponieważ or bo?

Dlatego is a coordinating adverb (“therefore,” “that’s why”) linking two independent clauses: the first clause gives the cause, the second — introduced by dlatego — gives the result.
By contrast, ponieważ and bo both mean “because” and introduce subordinate (dependent) clauses expressing the cause. You could rewrite with ponieważ:
“Ponieważ głośnik w tramwaju jest zepsuty, kurier nie usłyszał naszej decyzji.”
but then you drop dlatego.

Why is there a comma before dlatego, and is it always required?

The comma separates two main clauses:
1) Głośnik w tramwaju jest zepsuty (cause)
2) dlatego kurier nie usłyszał naszej decyzji (effect)
In Polish punctuation, you place a comma before dlatego when it functions as a link between two independent clauses like this.

What tense and aspect is usłyszał, and what is its infinitive?

Usłyszał is the 3rd person singular masculine past tense of the perfective verb usłyszeć (“to hear,” with the sense of completing the action). Perfective aspect is used because the sentence refers to a single, completed event (he didn’t hear it). The imperfective counterpart is słyszeć, which in the past tense would be słyszał (“he was hearing”/“he used to hear”).

Why is naszej decyzji in the genitive case instead of the accusative? Could we say naszą decyzję?

In negative sentences Polish normally uses the partitive genitive for the direct object. Here nie usłyszał (“did not hear”) triggers the genitive, so nasza decyzja (nom.) → naszej decyzji (gen.). Without negation you would use the accusative: usłyszał naszą decyzję.

Why isn’t there an article like “the” or “a” before głośnik in Polish?

Polish does not have definite or indefinite articles. You simply say głośnik for “speaker,” and context (or additional words) tells you whether you mean “a speaker” in general or “the speaker” in particular.