Learn Spanish (Spain): El ordenador ya no funciona. - The computer does not work any more.

In Spanish, when a machine, device, or system works (meaning it functions correctly), you must use the verb funcionar. The verb trabajar is only used for people or animals doing physical or mental labor.

How exactly does ya no mean "not any more"?

By itself, ya usually means "already" or "now." However, when you put it together with no to make the phrase ya no, it translates to "no longer" or "not anymore." Notice that this phrase goes right before the verb.

Is ordenador the standard word for "computer"?

Yes, el ordenador is the everyday word for "computer" in Spain. However, in Latin America, you will almost always hear la computadora instead.