Learn Italian: Il sistema non funziona a causa della disorganizzazione. - The system does not work because of the disorganization.

The compound preposition is a causa di (because of). Because it is followed by a specific noun (la disorganizzazione), the preposition di must combine with the definite article la to form the articulated preposition della.

Could we say per colpa della disorganizzazione here instead?

Yes, you absolutely could! A causa di is a neutral "because of" or "due to." Per colpa di literally means "through the fault of" and carries a negative, blaming tone. Since disorganization is a negative thing causing the system to fail, per colpa della would sound very natural here if you wanted to emphasize the blame.

Why is it il sistema? Doesn't the -a ending usually make a word feminine?

Sistema is one of several Italian words of Greek origin that end in -a but are actually masculine. Other common examples include il problema, il programma, and il tema. That's why it takes the masculine article il.

Could I use non lavora instead of non funziona to say the system "does not work"?

No. In Italian, lavorare is used for doing a job or physical labor (like a person working). When you want to say a machine, a system, or an idea "works" (meaning it functions correctly or is successful), you must use funzionare.