So any luck with your issue, or can you give a better description of the problem? It's all pretty vague. Is it turning ON from OFF or is the screen waking up and not going back to sleep.
In another thread I was just in, it sounds like the new phones are still shipping with JellyBean. With JB if you set an alarm, turned the phone off before the alarm, when the alarm time came the phone would turn its self on. It doesn't do this with notifications or alerts only the alarm. Only in the stock clock app, and only until you update to KitKat. They did away with this in KitKat, and I was a little sad to see it go. Maybe your other problem will go away if this isn't it when you upgrade to KK. Setting>Software update>Check new