You definitely need to provide log4net.dll to get Castle logging facility to work (assuming you have configured the logging facility to use log4net). You are correct that you no longer need to reference log4net directly in your projects, because you will now be using Castle.Core's ILogger interface to actually write log messages. Your application still depends on log4net, albeit indirectly.
Visual studio normally handles these kinds of "indirect" references (A depends on B depends on C) properly (it copies C over to A's output directory). However, it does not copy the indirect reference (it does not copy C to A's output directory) when C is in the GAC on the machine performing the build.
My guess is that you have log4net.dll GAC'd on your development machine.
To resolve this, you either need to remove log4net.dll from your GAC (and from the GAC on any machine where you'll be building the app), or you must explicitly reference log4net.dll in your top-level executable (project A in the example above) and set "copy local" to true. This forces the compiler to copy the dll to the output directory.
This issue was also discussed in this SO question