Learn Hardcore Russian: Без электричества лифт не работал, поэтому я поднялась по лестнице пешком. - Without electricity the elevator didn’t work, so I went up the stairs on foot.

The preposition без (without) normally requires the genitive case.
So электричество (nominative) → электричества (genitive): без электричества = without electricity.

Is Без электричества a full clause? It feels like something is missing (like не было).

It’s a prepositional phrase, not a full clause. Russian often uses this kind of “setting phrase” to give the circumstance:
Без электричества = With no electricity / Without electricity.
You could also say a fuller version like Не было электричества, и лифт не работал... (There was no electricity, and the elevator didn’t work...), but the given sentence is completely natural as-is.

Why is it лифт не работал and not лифт не работал(а/о) or some other ending?

Past tense in Russian agrees in gender and number with the subject.
лифт is masculine singular, so the verb is работал (masculine past).

masculine: работал
feminine: работала
neuter: работало
plural: работали

What’s the difference between не работал and something like не сработал?

не работал (imperfective) means wasn’t working / didn’t work (over a period of time)—a general state.
не сработал (perfective) is more like didn’t work (at one moment) / failed to activate—a one-time failure.
Here, не работал fits because the elevator simply wasn’t functioning due to the outage.

Why is поэтому used here, and why is there a comma before it?

поэтому means therefore / so / that’s why, introducing a result.
A comma is used because it separates two parts of a complex sentence:
[cause], поэтому [result].
In other words: The elevator didn’t work, therefore I walked up the stairs.

Could I replace поэтому with так что? What would change?

Yes, often.

поэтому = therefore / that’s why (slightly more “logical/explicit”)
так что = so / so that / as a result (often more conversational)

Example: ...лифт не работал, так что я поднялась... is also natural.

Why is it я поднялась (perfective) and not я поднималась (imperfective)?

поднялась (perfective) focuses on a completed result: you ended up at the top.
поднималась (imperfective) focuses on the process: you were walking up (without emphasizing completion).
In this context, the “result” reading is most typical: she got upstairs.

Why does the verb form поднялась end with -лась?

Two things are happening: 1) Gender agreement in the past: the speaker is presumably female, so past tense is feminine: подняла- + -сь
2) -сь is the reduced form of -ся, marking a reflexive verb: подняться = to go up / rise (oneself).

So я поднялась = I (female) went up.

If the speaker were male, what would change?

Only the past-tense gender marking:

female: я поднялась
male: я поднялся
Everything else can stay the same.

Why is it по лестнице? What case is лестнице?

After по meaning along / via / by (a route), Russian usually uses the dative case.
So лестница → лестнице (dative): по лестнице = by the stairs / via the staircase / up the stairs.

What does пешком add, if по лестнице already implies walking?

пешком means on foot and emphasizes that you didn’t take any vehicle/transport (and in some contexts contrasts with taking an elevator/escalator).
It can sound slightly redundant in English, but in Russian it’s a common, natural intensifier: I went up the stairs on foot (i.e., not by elevator).

Is the word order fixed? Could I say Лифт не работал без электричества?

Russian word order is flexible, but it changes emphasis.

Без электричества лифт не работал emphasizes the condition first (Without electricity...)
Лифт не работал без электричества is possible but can sound like “The elevator doesn’t work without electricity (in general),” more like a general statement.

For this specific situation (power outage), the original order is more natural.