First, grab a magnifying glass and a strong light and visually inspect the faulty port. Make sure that all the pins, especially the middle ones are there and that they are all straight and parallel with each other. Also ensure that there is no dust or lint in the port. Do not probe with anything metal in the port you may short out the power to the port. If there is dust use a vacuum cleaner to try and get it out. If there seems to be a problem with the pins the port will have to be replaced.
If that proves OK, go to Control panel > Device Manager, scroll down to USB controllers, click to expand. Then right click on each USB host controller and select uninstall. (Be aware that if you have any USB devices connected to a port when you uninstall it they will no longer work, until the USB host controllers have been reinstalled - see next paragraph))
Restart your laptop and let Windows 'find' and reinstall the USB controllers and then see if it works.
If not there may be a hardware problem with either the port or the USB host controller.