You can use could if you like. If the person you didn't call was in in some way responsible for your phone not working you might use could to show it was their fault. Using would is more of an apology.

Both would and could can be used in this sentence. Could is the past tense of the word can. So by using could you are implying that you could of called them earlier but you can't now or that somehow the ability to call them is impaired somehow. Of course, because your phone is broken in this case. Would is more used in situations that are more likely to have happened. Maybe in an instance where you were planning on call them but something happened that prevented you to do so. An example would be getting too busy with work.