I was finally able to get someone at my webhosting service.
It seems you were right in your initial assessments that it was all related to some new Gmail authentication requirements.
The Hosting guys gave me some new parameters for the DNS TXT field and I asked the guys at Site-5, who manage my Domain names, to add that info and they said they did it. They say that now it’s just a matter of waiting for the propagation to take effect.
I’ll try sending emails to myself from the Contact form in a few hours and I will let you know how it goes.
Just one last question, do I have to make any changes to the salaroche.com Contact page in order to use it for salaroche.net as well?
Thank you for your ultra-valuable attention and many thanks to Patrice as well.