I have had the same problem ever since updating to El Capitan.
Submitted feedback to Apple and waited patiently for an update to fix this "Major" problem.
Now After the Update OS X El Capitan 10.11.1 did NOT fix the issue, I found a solution that works for me.
Since None of the Sound features Now work for me in Mail except the "Mail Sent.aiff" for outgoing mail, I was forced to try "everything" including resetting Mail completely, but nothing worked, except this:
Using My same Rules in Mail I just wrote Apple Scripts to perform the functions I needed:
Here is an example of how to play a sound for New Mail:
Using the "Script Editor.app" in Applications/Utilities
Just open then select "New Document"
Enter this script:
tell application "Mail"
do shell script "afplay '/Users/MyAUDIO/BeepBeepBeep.wav'"
end tell
You will NEED to change the Path and the name of the sound file to one of your liking.
Use the "Play" arrow to test if the sound plays and test for script errors.
Just save the file to: "~/Library/Application Scripts/com.apple.mail" folder with a name like: PlaySound.scpt
Now, just go to the Mail "Rules" and use "Run AppleScript" for your Action.
If you placed your Script in the Folder above then it will be listed in AppleScripts Dropdown when creating the Rule.
Use something simple like: Check for "Any recipient" "contains" "@"
You should be able to get all your Rules working by creating an Apple Script to Perform the Action Instead using the "Built-in" actions that no longer seem to work...
Good luck!