Mail.app is immediately sending incoming mail into the Trash folder.

I am running OSX Mavericks on a 2007 iMac (Intel). The machine is completely up to date with all updates.

The problem occurs in Mail.app. It connects to three Gmail accounts, including my primary email account, which is in the gmail.com domain.

Until July 2, incoming mail was processed correctly, but beginning on July 3, ALL the mail incoming to my primary (gmail.com) account goes directly to the Trash folder. I have tried to ensure that there are no settings in Mail that are causing this; I didn't find anything. It is strange that this started so suddenly -- I suspect it was introduced through an update of OSX.

I tried sending emails to Gmail with Mail.app shut down, and the mail ends up in the Gmail online inbox, so I cannot imagine the problem is not in the mail processing by Mail.app.

Is there a fix? Right now I am unwilling to run Mail on my machine for fear of missing important mail.

Thank you.