According to the League of Legends Forums (here) you can try this:
Some sort of Maestro Error
- Restart your computer
- Temporarily Disable/Make exceptions in your Anti-virus/Anti-spyware software
- Temporarily Disable/Make exceptions in your Firewall
- Disable process protection software.
- Make sure you're running software in Administrative Mode/With admin privileges
- In Windows Vista/Windows 7, double check your Account Controls
- Reset your Internet Explorer Settings and make sure you have not disabled scripting options
One person solved it by going to
C:\Riot Games\League of Legends\RADS\projects\lol_air_client\releases\0.0.0.237\deploy
and setting LolClient.exe to run as admin.
One person updated Windows by running Windows Update and the problem was solved.
It's quite a common error and many people have odd ways of solving it. But since LoL and Steam don't connect I assume it's strictly connection or permissions.
Here's a video that explains how to fix the problem. (He explains the Maestro Error at 2 min 24 sec. It has to do with Anti-Virus ;) )
I've had this happen to me and it was the Anti-Virus I was running (Kaspersky btw). I tried white-listing it on the firewall, Virus list EVERYTHING and it still didn't work. The only way I managed it to work was to play with the Anti-Virus turned off. (But this was my personal case).
If you can solve it for LoL you will most likely solve it for Steam.
I wish you good luck! and I hope that I gave you some good things to try and fix the problem since we never know for sure what the solution is.