My iPhone 4S powers off after being unplugged
So last night my iPhone screen turned black and i plugged it in. The apple logo appeared on the screen, so I wasn't worried. The phone came on and I went onto instagram. There's no internet connection on any apps, even though we have wifi AND data. Also, my phone is about three hours and 10 minutes behind even though it says it's on the New York timezone (My timezone) It also says the year is 1970! The main problem is that when i unplug the phone, it immediately shuts off, even though the battery is 100%. After this, I can plug it back in and the process continues. Also, the phone will shut off after about a minute of being turned on, whether you unplug it or not. I've had the phone for about one and a half years and I have iOS 7. Please help!