I have had a problem running league of legends. I have an imac and i run the application using parallels. The program has worked before and i played it with friends multiple times, but now every time i try to run it i get an error message that says "Unable to connect to the server. If you have a firewall, it may be blocking the connection. Please refer to your firewall's documentation. Would you like to retry the connection?" I disabled my firewall and made sure that the game was on the allowable programs list and my internet connection is great, and it still doesn't work. Help Please!

The only thing I can think of is downloading hotspot shield. At my university, even with the firewall off and the game on allowable programs, I had the same problem as you, and since I've downloaded it it's worked great for getting patches and just playing the game. Here's a link, hope this helped out.
http://hotspotshield.com/