How to repair a USB port that won't accept a USB device?

I tried to plug in a USB cacble to my Toshiba Laptop and it would not go into the purt completely. The connection was not complete as the device I was trying to plug into the Laptop USB port would not work. I am not sure if the problem is with the Laptop or the USB connector on the device I was trying to plug in. How can I identify the correct point of failure? Would it be on the computer USB port or the usb device I am trying to plug in.

Once this is determined, how can I repair the USB connection, or does this require parts replacement?