I've tried to think of everything other than it being a faulty phone, but on certain calls the screen doesn't light up. There are two things I can do answer it not knowing who it is or try to power it up and that of course kills the call. I'm lost at this one, I'm hoping its a setting but I can't find one.
It seems it may be a software error on your device. I would recommend performing a factory reset to resolve this. the steps are listed below:
1. From the Home screen, pressthe Menu key .
2. Touch Settings > Privacy >Factory data reset.
3. Read the warning and touchReset phone.
Hope this helps.