Cant even open League (Alpha Client)

I have a Mac, all my windows are closed and I go to applications to open League. Then it says 'an older version was downloaded so it can be updated'...something like that.

Now the small rectangular loading screen says ETA 0 min. with 0.0 mb / 0.0 mb ...its been 4 hours now.

I know that my computer is slow for League of Legends already, but since I was able to use the Alpha Client, it has become unbearably slow... :(