Alarm or starter issues

I have a 2001 Volvo V70 T2.4 that I just got a week ago. On three separate occasions it wouldn't start. The first two times after repeated attempts then waiting for twenty minutes it started right up. This last time it will not. I turn the key and all lights and electronics come on, I hear a click, but the engine doesn't crank. New car battery installed already. The service engine light is on and there is a text which reads alarm system service required. The led for the alarm does go into rapid flashing once in a while until I reset using the remote. Not sure if it's a problem with the starter or its components or alarm or its components. Any advice?