Mail cannot connect to google account, won't open once quit
I had this problem yesterday and restarting seemed to fix the issue. When it came back today I looked online but couldn't find any answers. A look in the console showed that the issue was not network related, but actually caused by low disk space. Sure enough, making some space on my drive ( . . .was down to the bytes) immediately fixed the issue.

Moral of the story: Keep your disk clean!