For 4.0.4, you need a very old GApps package (2012–2014 era). Example: gapps-ics-20120429-signed.zip (for CyanogenMod 9).
Because the underlying security protocols and are obsolete, the Play Store app will likely throw connection errors or refuse to load any app listings. Even if the app opens, it cannot authenticate with modern Google servers. 2. Dropped App Support Most major apps have long abandoned Android 4.0.4. Android 4.0.4 Play Store