Why doesn't my iPhone 4 start up with a full battery and doesn't connect to wifi

Hi I got on my iPhone to find out that it would not start. I plugged the power cord in and it started but I unplugged it and locked it and it would not turn back on. While it was on I found out that it wouldn't connect to the Internet and wouldn't allow me to enable it. If someone could identify the proble that would be amazing.