If none of these works, you can always reflash the tablet. Then you can install skype with no problems. Of course, this is a drastic solution. But if you need it...

Ok, I think I know your problem. Check how much free space you have on the tablet. The problem is that there is not enough space to download anything, including the apt lists (which the app manager uses). Free up some space, and try again. Just remember, you cannot uninstall anything or install anything, because apt-get is now broken on you machine until you free up space.

Delete one of the videos or music that came with the tablet. That should do the trick

Or you could have a DNS problem *wink wink*