Hi and Welcome. My Name is ***** ***** I look forward to assisting you today with your question.
On Safari, go to www.gmail.com
Try to login there. Are you able to login ?
So, is Mail application asking for the Gmail password ?
Go to www.gmail.com and do you see all your emails there ? If all your emails are stored on www.gmail.com, then follow the steps below to fix it.
Go to Apple > System Preferences > Internet Accounts. If you see your Google account there, select it and press the - (minus) button on the bottom left. Then click the + button and add it back. This will re-establish the connection
Please let me know if that didn't work, so we can continue troubleshooting
Sounds like look you are using a very older version of OS X. Follow these steps below;
Open Mail and choose Preferences from the Mail menu.
Click Accounts in the Preferences window.
Select (highlight)your Google account on the left side of the window
Click the Account Information pane.
Re-enter your password *****
Then from the"Outgoing Mail Server (SMTP)" pop-up menu, choose Edit SMTP Server list.
Under Account Information, change the server to smtp.gmail.com (even if is already there,remove it and enter it again)
Click on Advanced tab.
Enter your full email address for username and enter your correct password (Make sure Password ***** ***** for Authentication)
Close it. Restart Mail.
Is it working now ?
If not, then follow the steps below;
Open Mail app. Click on Mail menu and select Preferences. Under Accounts, select you Google/Gmail account and then remove it by clicking - button. Then add it back there.
Please let me know if that didn't work, so we can continue troubleshooting.
Deleting and add the account should've worked. The problem is, Mac OS X 10.6.8 is very old and Gmail's security won't work on it. So let's try it again, but this time we need to enable something on Gmail, so the account will be added on Mail (this is necessary to add the account back since you are using older version of OS X)
Go this link on Safari --> https://www.google.com/settings/security/lesssecureapps
Next to "Access for less secure apps," select Turn on
Once you did that, Open Mail app. Click on Mail menu and select Preferences. Under Accounts, select you Google/Gmail account and then remove it by clicking - button. Then close Mail. Click on File menu and select Add Account. Then add it. This should work now.
Yes, we can continue later. Add a bookmark of this page or add this page to your favorites, so you can get back to later to continue this session
(Sign in to Gmail if asked)
If you have a few more minutes, try the above suggestion. It will take only a couple of minutes to do it.
There is also another way to fix it. If you upgrade the OS X to latest vesion (10.12 Sierra), then it will upgrade the security as well and this will allow you to add Gmail back. I will send you instructions now
Click on the Apple icon and App Store. This will bring App Store. Click Updates tab. If your Mac can handle latest OS X, then you will see Mac OS X Sierra there with FREE UPGRADE button. Click Free Upgrade and enter your Apple ID and password (this password ***** ***** from Gmail password)
This will downloa dthe update. It may take a few hours to download. Once the download is completed, it will bring the OS X Installer. Follow the onscreen instructions to install it. It may take up to 3 hours to install the upgrade.