Why Mail 7.3 can't connect to imap (gmail) ?

Hi,

I'm running Maverick 10.9.5 on an iMac mi-2010. All of a sudden, Mail 7.3 can't connect to the google Imap server. I have more than one account. None of them work anymore.

In fact, it began with SMTP problems that I finally solved, but only to see this new problem arise with the Imap server.

I think I've done all that could be done, after reading a lot of posts on the net, to no avail:

- checked all the settings (name, password, SSL and ports) multiple times (in Mail preferences) and in the general settings (internet accounts) of Maverick;

- checked the settings on my Google accounts (Imap enable, 1 step authentication);

- erased my account (in Mail) and created a new one, manually (not with the option "Google"): it never worked, couldn't download any of my currant emails;

Any help would be greatly appreciated !!

Thanks