Can't get gmail account online. After changing pw, made change in Mail settings, but keep getting "Unable to Connect'' error msg. Help!

I have a MacBook Pro using Mac OSX Lion 10.7.5, with 2.53 GHZ Intel Core 2 Duo processor, 249.2 GB storage capacity.

I got an email from Google saying someone tried to sign in to my gmail account from an app, and Google prevented it. As recommended, I changed my password. I then went on Apple Mail and changed the pw there, but the account remained offline. I went to gmail's support community and followed advice, re-entering my information under "Edit SMTP Server List'' but without success. This is the error msg I continue to get:

There may be a problem with the mail server or network. Verify the settings for account “Margaret's email” or try again.The server returned the error: Mail was unable to log in to the IMAP server “imap.gmail.com” using “Password” authentication. Verify that your account settings are correct.

Please tell me what to do to get access to my gmail account via Mail on my Mac. Thanks.