It's either hardware (the microphone itself), or software (driver) or a setting (mute, or volume 0, either on system level or in Skype).

The usual way to reinstall a driver is to download it from the makers site (for example or or whatever) and then install it according to the instructions. There's no standard for that, and it's no sure it will help, if there's no exclamation mark for it in Device Manager. But maybe, if you let Microsoft update it, it helps (tip: set Windows update to never update drivers).