CyanogenMod 10.2.1 - Google Play Store refuses to connect

I rooted my Samsung Galaxy S4 today with a fresh CM 10.2.1 ROM, and I cleared all the data and caches via CWM recovery before doing so. I also flashed the appropriate Gapps ZIP (20130813) for that version. I was able to login to Google at startup. However, the Google Play Store would refuse to connect, giving me the dreaded "No Connection" error. I tried EVERYTHING, including adding the IP for the Android Google Play servers into the hosts file, which just changed the error message to "Connection timed out." I even tried wiping my phone and re-flashing both of them.

Remove the google account and then re-add the account. This was how I fixed this issue.

Go to /system/etc/ and open hosts, delete or comment out anything connecting to google.