I'm not sure if it's the original battery or not.

I just got a call back from the dealership saying that they have a diagnosis. They're saying that there are two issues. The first is that the key is basically bad so they have to replace that. And also that the ignition cylinder is grinding into the housing, so they're going to have to replace that.

Does this make sense as to why the alarm would keep going off though? Anyone have any ideas about how legit the diagnosis is?