My iPhone 4S won't charge or turn on

I have an iPhone 4S, and have recently encountered some problems. The phone was a hand-me-down from my dad, so we replaced the back and battery. Everythingwas workingfine for five months. The phone itself is about three to four years old.

Recently, as I was going up the stairs, my phone fell and crashed on the floor, and the back popped off and the battery fell out (but still remained attached to its cable). After popping the battery back in and connecting it to my desktop computer, the phone continued to work fine.

However, last week, the phone spontaneously didn't turn on. It had been working fine up to that moment, with full battery and everything. I had turned it on quickly to check the time literally less than a minute before. After about three hours, the phone resumed working, as if nothing had happened.

That is, until today. My phone wouldn't turn on again, having been working fine right up until then. I assumed it was something like what hadhappendpreviously and didn't worry. However, after the time duration had gone way past that of the first time I started to worry. I tried restarting/resetting it, connecting it to computers, and connecting it to wall chargers. Nothing was working, until just now. I plugged itin tomy wall charger again and the Apple logo came up. However, even then it randomly shuts off and begins the restart process again, and when I do make it to my home screen I have no WiFi, data, or service, and it will only restart or turn on when connected to a charger (even though when I do make it to the home screen, it says the battery is at 100%).

Are there any other measures I could take or is my phone dead?

Sorry as to how long this is...