I have the exact same problem. I was on a Rom stock 4.0.2 with root, and after flashing the OTA, I had the problem when the screen is off.
To be sure I flashed the factory image in 4.0.4 but I still had the problem.
I looked at logcat and I had this error that seems to be the problem:
Code:
03-30 15:58:16.639 E/ConnectivityService( 186): Exception trying to remove a route: java.lang.IllegalStateException: Unable to communicate with native dameon to add routes - com.android.server.NativeDaemonConnectorException: Cmd {interface route remove rmnet0 default 10.114.222.1 32 0.0.0.0} failed with code 400 : {Failed to remove route from default table (No such process)}
03-30 15:58:16.639 E/ConnectivityService( 186): Exception trying to remove a route: java.lang.IllegalStateException: Unable to communicate with native dameon to add routes - com.android.server.NativeDaemonConnectorException: Cmd {interface route remove rmnet0 default 0.0.0.0 0 10.114.222.1} failed with code 400 : {Failed to remove route from default table (No such process)}
I'm going to send my phone to repair and hope they change it, or if someone has a solution.
Right now I flashed the 4.0.2 factory image to be able to use my phone.
PS : maybe someone know how to contact a Google dev ? To report the problem to them ?