Breakdown of Без электричества лифт не работал, поэтому я поднялась по лестнице пешком.
Questions & Answers about Без электричества лифт не работал, поэтому я поднялась по лестнице пешком.
The preposition без (without) normally requires the genitive case.
So электричество (nominative) → электричества (genitive): без электричества = without electricity.
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.