|A very long shot (actually two); both of which I have found to produce a similar effect to that which you describe.|
Check the date on the problem computer; that is not set in the future. I had one occasion where that had happened - the date had been set (somehow) to a date in the near future. Outlook canto send mail back in time...
Some anti-virus utilities can/will block out bound mail; Avast (is one that) will on some versions of windows (and Mac OS) and with some versions of Outlook block outbound mail.
Temporarily disable email screening... if the option exists in your anti-virus utility; and see if that resolves the problem.
Also (a third long shot) check firewall settings?
Perhaps use a working system as a model for the problem one; and compare settings various between the two systems?