Can't login with Gmail App/Play Store on tablet; Username/Password OK on desktop web browser
Did u set 2 step verification to your Gmail account? If yes then you need to set Application Specific Password to your account. 


Login to your Gmail from Desktop. 
Goto Settings page. 
Find Authorizing Application &amp; sites page. 
Goto Application Specific Password section 
Set your app name and device and Password, then click Ok. 
Now you can login to your app with that new Application Specific Password. 


For more help visit this page. 

https://support.google.com/mail/answer/1173270?hl=en