Hello and welcome to Android Forums. Hopefully I can help you with your problem.
Ok, 1st off make sure that you are getting signed into the Google Play store. That will confirm that you are indeed signing in with the correct password. You will then need to go into your device settings and make sure that you tap on your Google account and make sure that you have everything checked to sync that you want to sync. You may in facty need to manually sync it the 1st time. Hopefully that will sync everything that you have checked to sync.
If you have made sure that the password is indeed correct and you are signed into Google Play and you still canot get it to sync, go into phone settings/ updates and tap on update profile. This may take a few minutes while your profile is being updated. After this has been done, turn off your phone and pull the battery for a minimum of 1 minute. Personally, I leave my battery our for aprox 2 minutes. Aftewards, place you battery back in your phone and reboot. Make sure you give you phone ample time to completely reboot. This is paramount.
After you have gone through these steps making sure that your Google account is set up and sync is turned on, check Gmail and see if it will sync. Also check your contacts and calendar to make sure that they are syncing. If your device is still not syncing, contact your service provider and tell them what is going on. It may be an issue on their end.
One more thing that I forgot to mention that is very important!!!! If you are running a firewall, make sure you have sync enabled.
I hope this helps get you straightened out. If not, please start a new thread stating all the steps you have gone through in order to try and get the phone to sync. Hopefully this will not be necessary and the steps I have given you will work.
Thanks and best of luck getting your device to sync.
WB7
If you have any other questions regarding your device, I invite you to join Android Forums. We have many sections for specific devices which contain a wealth of information.