iPhone Shuts Off and Greyed Out Wifi?

I have an iPhone 4. iOS 7.1. No phone carrier, I ONLY can use it with wifi.

My iphone has always been a little off, but it generally always worked well. Today, I saw my battery was down to about 20% so I plugged it in. It was working fine, I was using it while it was charging. When it got to about 50%, I unplugged. I didn't use it after I unplugged it and when I looked back about 5 minutes later, it was off. I plugged it in and it turned right on and was working perfectly, despite being unable to connect to wifi. I unplugged it to bring it closer to the router, but as soon as it was off the charger, it went black. It refused to turn on again until I plugged it back in. This time when the phone turned on, everything was bad.

It said it was at 100 percent charged, which is impossible since it was just at 30%. The time and date are random now, saying its January 31st. Every time I unplug it now, it automatically shuts down. Even when its on the charger, the screen flashes grey and it restarts itself every few minutes (about 2-3 minutes). The wifi is also greyed out and I am unable to click it.

I tried resetting the settings, but it didn't do anything. I really would like to avoid deleting data, as I have no way to save my photos. My iphone has taken some nasty falls and gotten wet, but it never seemed effected by these. It has always had a very impressive battery life compared to my friends phones. Today when it stopped working, I had done nothing to it, didnt fall or anything. Really would like to see some fix of this issue!

thanks!