Android's Add Google Account Problem:How to fix it.

This is the popular message happens when one try to sign in to the Google play Android Market,
fortunately this is the pretty little problem.
the problem can be solved in consideration to the following ways:
   First of all you must make sure you have a valid connection to the internet either wi-fi connection or mobile data connection.
Then make sure there are no any running applications that prevents data from incoming or outgoing to and from your mobile phone respectively such as firewall or security applications.
In assessment to those, check the following setting.
Go to Setting>Date and time, Verify the date and time and make sure they are accurate.this solution doesn't often work but most of time it is the vivid solution since the internet connection depends mostly on your device Date and Time.
but if that doesn't work Go to Setting>Account and Sync, then check the background data and also the Auto-Sync on the check box.
you can also go to Setting>Applications>Development and you might want to turn on "Allow mock locations"
I have used these ways several times and have successfully worked.
I'm sure your problem should be solved on reference to the provided brilliant solutions.