This post is for anyone trying to use Skype video and having the problem where one party can't see the other. That is, audio works fine and video one-way works fine, but just not two-way.
I've had this problem a few times with my parents and it is really annoying. We could see them, but they could never see us.
The short answer is this issue has always stemmed from a firewall problem. As such, messing with firewall settings has always fixed it.
It took so long to fix (for us) because I didn't immediately think firewall problem because audio and one video stream worked fine. So I kept looking at Webcam settings and drivers, and things having to do with Skype itself. No help there.
You should have the firewalls on both sides open to Skype. Ideally, you should port forward specific ports for Skype to the relevant computers. Doing so will ensure zero relays and increase your chances of high-quality video working correctly, as I outlined in a previous post.
The quickest solution is to set the Skype computer as the DMZ in your router/firewall. I don't recommend this long term for security reasons, but it's good for testing.
Also, remember to also check any software firewalls, e.g. on your operating system (OSX, Windows, etc.). The problem can also lie there.
Finally, doing these somewhat complex settings on a remote computer like my parents' computer can be tedious. I currently use Crossloop for messing with their computer, which is free and is easy enough to download and use that they can do that part.