Chosen Solution

The phone would restart randomly and/or shut down completely even when showing at least a half charge. It became worse and completely shut off and would not start past the apple logo screen. I replaced the battery. Phone will not start past the apple screen. I attempted to restore , the phone attempts to restore with the progress bar under the apple and then I get “error 9” in iTunes saying phone cannot restore. Any ideas what is probable broken?

Probably a bad replacement battery. It is hard to find good batteries so I recommend buying one from iFixit. And use 3UTools (http://www.3u.com/) to exit recovery mode boot loop, the system software on the phone is probably still fine.