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When you connect your cell phone apps to a bunch of account that are using your Google (gmail) account as the main account name, and then you delete that account from existence, the phone will start to have problems.
However, I am not certain that I fully understand what the issue is. Did you completely delete your Google account? Or did you just delete/remove the Google account from a configuration on your phone?
If you can give me some more specific details, I am sure that I can assist you.