Either your sim card is not seated correctly, the contacts are dirty, the sim card is dead, the copper contacts in the phone do not reach the sim card or the electronics in the phone are faulty. try to change a new battery' or maybe the sim card driver is unsoldered' or need to replace. here is the pics. skilled technician can do.
When we connect the phone to PC it automatically start charging but after 5 mins it stops its because we do not take any kind of action i.e. if you will send some files to phone or will operate phone from PC it will keep charging otherwise as you have said it will stop.
Source: Charge by usb cable