First I memorized the meaning of no sirve as "doesn't serve" (its purpose). Then I came across an explanation on the difference between "no funciona" and "no sirve" that said they mean "doesn't work" and "isn't any good", respectively. (If I remember well, I read this on duolingo somewhere, but I'm not sure.) Now this lesson made me totally confused. Googled it and found various explanations. The majority says that no sirve can mean that it does not work at all; and also can mean that it works, but not that well. Other hits: badly designed, not really useful.
Or "The telephone does not serve it's purpose." Yes? Like some other people here, due to my technical training, background and education I tend to think that "functiona" would be a better way in the Spanish language than "sirve". However, given the fact that not all people are technically oriented "sirve" would also convey the same concept via the written and spoken language of both Spanish and English. In other words I can understand how the use of both words can be considered completely acceptable in order to actualize the thought.
Trabajar means 'to work', as in 'to labor' - it refers to something a person does. Servir means 'to serve', and I think that also means something that a person does, as opposed to what an inanimate object (such as a telephone) does. I don't agree with Duolingo's use of the words in the sentence, and in my opinion the correct translation for a telephone that is not operable, or out of order is "El telefono no functiona".