Hi,
Who is your ISP (Internet Provider), as special settings are often required in your Outlook 2010 account setup. I've been an E-mail administrator at dozens of companies. Can you use a browser (Edge, Chrome, IE11) and go to gmail.com and login with your new, the 3rd Gmail account, and your password there? If so, then it's not an account issue or a problem with your account password. Most likely a problem with the manual settings within your Outlook 2010 program. You should look at the manual settings for your other 2 Gmail accounts, copy those done with pencil and paper or use your Cell phone camera to snap photos of each of the various settings pages. Go back into the 3rd Gmail account settings in Outlook 2010 and duplicate...