Hi there and welcome Edwin
Can you please go to Settings, Applications Manager.
Navigate to the list ALL and locate Google Play Services.
Press it and press clear data.
Once done, restart the tablet and tell me if Gmail now works please.
To the tablet I cannot sorry, but you need to swipe to the list of ALL under Apps manager
ok, you need to though press clear Data please
No, it means the service then is corrupted and needs to be remade.
To do this you will need to reset the device.
This is going to remove all data and return the device to new, so any photos ect you have on it you will need to backup
Emails it will download once the account is added again.
To do the reset, go to Settings, Backup and Reset.
Press on Factory Data Reset.
Complete the reset and when it is done, set up the device again and it should now function
Let me know the results please.
If you would like any additional information or assistance, please do not hesitate to let me know.
and please take a second to rate my service by clicking one of the stars at the top of the screen then submit