If the store opens but won't let you sign in or browse apps, your Google Account authentication token might be outdated.
How to Download and Update Google Play Store on Android 4.4.2 (KitKat) Download Google Play Store Android 4.4 2 %28%28LINK%29%29
While strictly a website, APKMirror is the safest bet for downloading individual APK files for your older device. It archives thousands of apps and, crucially, offers older versions of apps. This is invaluable for Android 4.4.2, because newer versions of modern apps often require Android 5.0 or higher to run. If the store opens but won't let you