A little late but I was having this problem too and running studio as root just created more problems (using OSX here).
I fixed it by manually installing what was failing to install using the Android SDK manager. Just run android sdk
in a terminal (probably the same on Windows but don't quote me). Let it install all the updates it wants, then if you can't make it through the setup, manually find the packages that are failing to install and install them.
Got me through a very frustrating problem and back to work.....