Похоже, батарея не работает, поэтому в комнате холодно.

It seems the radiator isn’t working, so it’s cold in the room.

Breakdown of Похоже, батарея не работает, поэтому в комнате холодно.

• в: in
• комната: the room
• не: not
• работать: to work
• холодно: cold
• поэтому: so/therefore
• похоже: it seems
• батарея: the radiator

Questions & Answers about Похоже, батарея не работает, поэтому в комнате холодно.

What does похоже mean here, and why is it used with a comma after it?

Похоже means it seems / apparently / looks like. It’s used as an introductory (parenthetical) word, so it’s typically set off by a comma: Похоже, ... = It seems that....
You can also say Похоже на то, что ... (more explicit), but Похоже, ... is very common in speech and writing.

Is there an implied что after похоже?

Yes, conceptually. Похоже, батарея не работает corresponds to Похоже, (что) батарея не работает = It seems (that) the radiator isn’t working.
Russian often omits что after introductory words like похоже, кажется, думаю, especially in everyday style.

Does батарея mean a “battery” (like in electronics) or something else?

In this context батарея almost certainly means a radiator / heating radiator (the thing under the window). That’s a very common everyday meaning in Russian.
It can also mean an electrical battery, but paired with в комнате холодно (it’s cold in the room), the heating meaning is intended.

Why is it батарея (nominative) and not another case?

Because батарея is the grammatical subject of не работает: (The) radiator doesn’t work.
Subjects are normally in the nominative case.

What does не работает literally mean, and what tense/aspect is it?

работать = to work / to function.
не работает = is not working / doesn’t work (present tense, imperfective).
Imperfective in the present often covers both “right now” and “in general,” but here it naturally reads as currently not functioning.

Could I also say не работает батарея? Does word order change the meaning?

Yes, Не работает батарея is also correct. Word order mainly changes emphasis:

• Батарея не работает: neutral, “The radiator isn’t working.”
• Не работает батарея: emphasizes the failure/issue first, closer to “The radiator isn’t working (that’s the problem).”
  Both are common.

What is поэтому, and how is it different from потому что?

поэтому = therefore / so / that’s why (it introduces a result).
потому что = because (it introduces a cause).
So you get two opposite directions:

• Cause → result: Батарея не работает, поэтому в комнате холодно.
• Result → cause: В комнате холодно, потому что батарея не работает.

Why is there a comma before поэтому?

Because it links two parts of a compound sentence:
[It seems, the radiator doesn’t work], therefore [it’s cold in the room].
In Russian, a comma is normally required before connectors like поэтому when they connect two clauses.

Why is it в комнате (prepositional case)? What does it literally mean?

в + location answers where? and takes the prepositional case: в комнате = in the room.
комната (nom.) → комнате (prep.).
If it were motion “into the room” (where to?), it would be в комнату (accusative).

Why does Russian say в комнате холодно instead of “the room is cold”?

Russian often uses an impersonal structure with an adverb of state: холодно = (it is) cold.
So в комнате холодно is literally “In the room, (it is) cold,” meaning “The room is cold / It’s cold in the room.”
This is very natural Russian, often preferred over комната холодная (which describes the room as “a cold room” more like a property).

What part of speech is холодно here?

холодно is an adverb used in an impersonal “state” construction (often taught as category of state / predicative). It functions like a predicate: (it is) cold.
Related forms:

• холодный (adj.) = cold (e.g., холодная комната)
• холодно (state) = it’s cold (e.g., мне холодно, в комнате холодно)

Can I replace похоже with кажется? Is there any difference?

Often yes: Кажется, батарея не работает... also means It seems (that)...
A common nuance:

• кажется often sounds more personal/subjective (“it seems to me”)
• похоже often sounds a bit more “based on evidence/appearance” (“it looks like…”)
  But in many everyday contexts they are interchangeable.

Is this sentence more like spoken Russian or written Russian? Anything stylistic to note?

It works in both. The structure is very natural in conversation: Похоже, ... поэтому ....
If you wanted a slightly more formal/explicit style, you might add что or use похоже на то, что..., but the given version is perfectly standard and common.