free tool to do basic color correction?
The cheapest tool is to use a desk lamp and light the scene better to begin with and use the white balance setting in the webcam software itself.  It's a lot harder after the fact (if sufficient detail is even saved in the video to fix it at all).  

You could also try DaVinci Resolve Lite, it's a professional color grading and correction package that also happens to be completely free, but the much better solution is to light and shoot correctly rather than trying to fix crappy footage in post.