If it's Fatal Error (4): Null, then I'm sure it's avira or mcafee's internet security filtering the connection.
If it's Fatal Error (4): unable to get imput stream for lwjg_applet.jar.pack, it's antivirus. If it's AVG, disable Linkscanner.
If it's Fatal Error (4): Path to .minecraft\bin\minecraft.jar, clear the .minecraft folder, usually corrupt file.
If it's Fatal Error (4): Address family not supported by protocol family: connect, they have malware on their computer.
If it's Fatal Error (4): Permission denied: connect, they're likely using Java 7. Uninstall, reinstall java 6.
If it's Fatal Error (4) on classic, clear the browser's temp/cache files. If it's IE on windows, clear %temp%\www.minecraft.net\ and %temp%\minecraft.net
If it's Fatal Error (4): unable to get imput stream for lwjg_applet.jar.pack, it's antivirus. If it's AVG, disable Linkscanner.
If it's Fatal Error (4): Path to .minecraft\bin\minecraft.jar, clear the .minecraft folder, usually corrupt file.
If it's Fatal Error (4): Address family not supported by protocol family: connect, they have malware on their computer.
If it's Fatal Error (4): Permission denied: connect, they're likely using Java 7. Uninstall, reinstall java 6.
If it's Fatal Error (4) on classic, clear the browser's temp/cache files. If it's IE on windows, clear %temp%\www.minecraft.net\ and %temp%\minecraft.net