Translation:They will not respond to the message.
Well it uses "Nachricht" singular, which is "message". Although it can be "news", the plural form "Nachrichten" is far more frequently used for that.
Anyway, "not answer the news" would be "Sie werden den Nachrichten nicht antworten."
In this case it uses "antworten auf", which means "to reply to" or "to respond to".
While it is true that two-way prepositions such as auf take the accusative if they show motion, I don't think that is exactly the rule. As I understand it, they use dat. when they show "position, location or non-'motion' condition" (be that physical or temporal) rather than when they "don't show movement". In other words, it isn't "if motion then use acc; else use dat" but rather "if static/explicitly non-motion then use dat; else acc". Auf does not indicate that die Nachricht is in a place/time so takes the accusative. Bear in mind however that I'm also a learner, so could well have misconceptions here as well.
I was wondering the same thing a few days ago. It turns out that any usage of the two-way prepositions that is unrelated to location/position takes the accusative.
When relating to location but not involving motion, they take the dative. When relating to motion, they take the accusative. In any other situation, they still take the accusative!
I was wondering just the same since I encountered a few sentences here where they used the dative/accusative when it didn't have anything to do with movement, but then I read canoonet's explanation: http://www.canoo.net/services/OnlineGrammar/Wort/Praeposition/Kasus/2Kasus.html?lang=en
The rule of implementing dative when referring to static states and accusative when referring to motion and movement does apply in general, but apparently every preposition has its own rules any nuances in cases where it isn't about 'static' or 'motion'.
Their explanation for 'auf' clarifies the implementation of the accusative case in the sentence above.
Not sure what you mean, it's the noun, as in "a report".
"Ich lese einen Bericht." - "I read a report."
The verb version, "to report", is either "berichten", "melden", among others.
"Der Reporter berichtet über die Verhältnisse." - "The reporter reports/is reporting about the situation."
Ah. "Bericht" covers basically all uses of the english "report", (as a noun.), e.g. "account", "review", "bulletin", "statement" etc.
"Nachricht", however, has a number of uses confined to things like "message", "news", "communication", "information" etc.
So it's definitely plausible that you would hear them both on the German news haha.