I had issues a little while ago with adding a microsoft account, it turned out the default user account was corrupt. I had to copy the default profile from another machine (windows 10 in my case). That fixed my problems, might be worth a shot?
That pop-up looks like a modern authentication window. You could try disabling it by adding the following registry key: [HKEY_CURRENT_USER\Software\Microsoft\Office\16.0\Common\Identity] "EnableADAL"=dword:00000000
I don't suggest this as a long term solution, but at least you will know if it's related to modern auth or not.
I am getting the very same problem today. I turned off my computer on Friday, turned in on today and tried to read some e-mails but it did not start. I have windows 10 installed on a macbook pro via bootcamp and had no problems for the past 2 years with outlook 2016.
I uninstalled all office programs, re-installed again but it did not work. I then formatted by computer/windows and downloaded office365 64-bit from scratch. All applications work except outlook. I get the same 'something went wrong' issue when trying to setup my e-mail.
Is there a solution for this one? Microsoft we need your help urgently!