I checked out Christopher's suggestion of deleting my gmail password in the keychain when I discovered that there was a separate google password.
IOW: mail.gmail.com and mail.google.com
When I deleted the gmail entry, I was able to use the accounts page from sysPrefs "Internet Accounts" to select all of the services including mail.
I then went to mail and ensured that the google account was enabled. This immediately downloaded all my imap emails.
However, I had to quit mail and restart it to send emails.
WARNING: when I was trying to use my gmail.com password that I found in the keychain, I had no idea there was also a mail.google.com password. I had changed the mail.google.com password 3 months ago when I upgraded to Yosemite on my old MacBook Pro. So this morning when I tried to get "gmail" to work on my new MacBook Pro through either the Internet Accounts screen in SysPrefs, or through the Preferences in Mail, it failed -- without explanation!
Having forgotten the mail.google.com account, I changed my password (Let's call it PW3) using the google web pages, I was able to log onto the web pages. After I had deleted the entries for mail.gmail.com and smtp.gmail.com (which used PW1) and accessing my google-mail account through Mail.preferences (which opened the Internet Accounts Screen in SysPrefs), Mail used my mail.google.com (PW2) to download all my emails.
So, I've deleted PW1 from the keychain (gmail.com)
I've discovered PW2 remained in the keychain (google.com)
I have PW3 @ the google web page. (aggh).
So, I created a PW4 which I changed using the google web pages.
About 10 minutes later, a dialogue box popped up that asked if I wanted to save that PW.
I now also have a keychain entry for: myaccount.google.com (email address) in addition to the mail.google.com PW.
All the passwords seem to be working.