Changed gmail password now I can't get mail on computer

Here's something you might try. It works for me, your mileage may vary. I'm running 10.10.3, have a couple week old MBP and this is how my email setup worked both when new and after I did a couple restores. In short, my OS X mail account was automagically created.

1. Go to Google with Safari and make sure you're logged out.

2. On your Mac go into System Preferences > Internet Accounts.

3. Highlight your Google account and hit the minus sign at the bottom to delete it. If prompted to confirm, say yes.

4. For the heck of it, restart your Mac.

5. Start up Safari, go to Google.com and log in.

6. *If* your system works like mine, after you sign in a dialog will pop up saying something like "Would you like to add this account to your preferences.

7. Tell it Yes.

8. It will take you back to System Preferences > Internet Accounts where you can check what you want to keep in sync. I turned on Mail and Messages.

After that, my OS X Mail App was up and running with my Google Gmail account.

-jeff

Mail>Preferences>Accounts>Your gmail account>change your psswd to your new passwd.

SMTP Outgoing mail server>Edit server LIst> change psswd

Did you try Mail > Preferences > Accounts tab and entering your new password?

-jeff

Repeating the same thing does not make this any clearer. After you changed the password at the Gmail website did you change it (in 2 places) on the Mac, once for IMAP and once for SMTP. Are you using Gmail 2 factor authentication?

Apple did not change your Gmail password, it's a user problem not an Apple problem. Please answer the questions I asked.

And you have entered the 2nd factor as well as the password?