Authentication error - GTalk in Android 2.3.6 in Samsung

[DroidExplorerGuntur]

I am trying to download an app from play store and I see this error: Authentication is required.You need to sign in to your Google Account.

But I have already logged in with my google account in the android phone after factory reset.

After going through alot of stuff online, I understand I missed something in the app for gtalk.
This is android 2.3.6 version in Samsung Galaxy Ace Duos handset.

I am neither able to find the apk file for gtalk to install it.
Can geeks suggest me how do I overcome this issue? I suspect if I have messed up with settings of applications ., pl see screenshots how they are in my phone now. I am unable to repair this. need some one's help:

--Help me--

 

[Parayilhussain]

Remove SD card.
Remove Sim card and insert back.
Go to settings >storage>cached data>clear cached data.
Go to settings>storage>apps>download manager>clear data.
Go to settings>storage>apps>>settings>clear data.
Go to home screen select"google settings" app>tap on this>three dot menu.
tap on the button" clear app data".
Uninstall updates in google play store.
Uninstall updates in google play services
Leave the device switched on overnight connected to a stable WIFI/WLAN .
With sufficiently charged battery.
The apps updated automatically.
Finishing this.
Reboot /restart device.