Ultimately, the Android 4.0.4 Play Store represents the moment Google stopped treating Android merely as an OS for geeks and started building an ecosystem for the masses. It was the stable, functional bedrock upon which the explosive growth of the Android ecosystem was built in the subsequent Jelly Bean and KitKat eras.
Log into the Google Play Store on a desktop browser. Find an old app (e.g., "Angry Birds Classic"). Click "Install" and select your Android 4.0.4 device. Often, the server will push the legacy APK even if the Play Store on the phone claims it's incompatible.