There's no reason to use past continuous here, so don't say "wasn't working". "Didn't work"? That's okay, but the natural way to say this is "My alarm didn't go off." (but alarms don't just fail to go off. The phone either died because you didn't charge it, or you set the alarm incorrectly.)

My alarm didn't work this morning - Simple Past My alarm wasn't working this morning - Past Continuous

1. happened and finished. 2. still not working, start on the past and continuing

1. the first one is past simple >> an action or something happened in the past and ended 2. the second sentence is past continuous >> an action or something happened in the past and still not finished till now 3. so the first sentence is the right one .