The Play Store often fails if is also outdated.

: The Play Store often won't run without a matching version of Google Play Services

Updating the Play Store on Android 4.2.2 is not as simple as hitting an "update" button within the app settings. It requires a manual installation process known as "sideloading." Here is a guide on how to safely download and install the Google Play Store APK for your Android 4.2.2 device.

Android 4.2.2 ya no es compatible con las versiones más actuales de la Play Store (como la v51.0). Debes buscar versiones etiquetadas para (API 16):

After installing the new Play Store: