Why won't my phone open any Google apps?

[AC Question]

The phone was unlocked from Metro PCS to WalMart Family Mobile (powered by T-Mobile), and I'm told that the Google apps worked before I unlocked it. When I obtained the phone, I unlocked it and rooted it right away (this isn't my first rodeo). But now the phone will not communicate with Google AT ALL. I used a KitKat launcher and a Lollipop launcher (its an LG F3) to see if I could get Google going by updating the Android version the phone was running - nothing. Instead of the rainbow icon, the Google logo in Google Settings is grayed out. I CANNOT sign in. Google Play, Hangouts, Gmail - none of them open AT ALL. They start to, and then cut off, no error message. I have tried EVERYTHING that is published online already, including editing the hosts file and even deleting it. Factory reset, you name it. In no way can I sign into a Google account or add one because whenever I try, the function shuts down before I can even get to a login field or screen. The option no longer exists.

Why does my phone refuse to communicate with Google? Does anyone have any experience with this?