I only interviewed via Skype once and that was 2 years ago when I was away and luckily, they agreed to do the interview. I echo those who say to practice through a friend or acquaintance. Pay special attention to their comments on how you sound and look. I would include the window that allows you to see the image they see, so you'll always know you're in frame.
From my personal experience, since there was a technical issue that delayed our start, make sure you have an alternate way of contacting them. A phone number would be preferable. If the technology fails you want to at least be able to call them and let them know what's going on, even if the problem is on their end. It might not be a bad idea to have another video service ready to go in case Skype gives you problems. Something like gChat or YahooChat. Even under the best of circumstances, it seems I always need a few minutes to make sure everything is working fine.
While I agree buying a new computer is not feasible, you might want to check with friends to see if anyone has a newer laptop that you can borrow for the interview. That would give you more options of where you wanted to be during the interview, if there is a better place than the dining room, and it would be a bit more reliable. Preferably a laptop with a built-in webcam so there is less issue of having the computer recognize it.