If you install the APKs but cannot sign in, it is likely due to outdated security protocols.
Be very careful when downloading system APKs. Files from unverified sources can steal your data. Stick to APKMirror whenever possible. google play store android 42 2 apk install
If you want, I can:
Here is a guide on how to download and install the Google Play Store APK, along with important safety information. If you install the APKs but cannot sign