When you try another cable, make sure that works with another device, and not just for charging.
The below instructions will help you troubleshoot if there is a problem with the usb connector on your phone.
1.Power off and disconnect usb cable.
2.Press and hold vol up and down, then hold the power button.
3.You should come to a boot mode selection menu.
4.Press vol down twice to highlight AP fastboot, press vol up once to select.
5.You should see AP fastboot flash mode (s), with last 2 lines saying "Connect USB, Data Cable"
6.Connect your USB cable to your PC and phone, and see if it says USB connected.
7. If nothing happens then it's probably a hardware problem, get it repaired.