Let's start out by seeing if the phone will tell us what's wrong with it. Go to the Kernel Panics wiki page and follow the instructions to check for panic logs. If there are any, download the latest one and add the first page or so of it to your question.
[[iPhone Kernel Panics|iPhone Kernel Panics - iFixit|new_window=true]]
[guide|21499|Adding images to an existing question - iFixit Repair Guide|new_window=true]
Either a screenshot or copy n paste will work fine. If there are more than one panic logs check to see whether they're showing the same error or not; if they're the same ignore the older ones but if they're different we might want to see them as well.
Once we have the logs or have confirmation that there aren't any we can figure out what to do next.