OK, I've found the problem.
Basically, I'm using this service under a two-week trial period right now. After doing a little digging, I figured out that they block port 25 during the trial period. Once I'm a paying customer, the restriction will be lifted.
A big thank-you to Jan and Falco for all your help. As they say over here, どうもありがとうございました。色々お世話になりました。m(_ _)m