"Dial failed, do you want to retry?"
I finally managed to solve the problem by going to Services and setting the Telephony Service to "automatic". For some reason it was disabled, that's what caused the error message.
So if you are having the same problem, make sure you try the solution I used. And if it works for you, please comment on this post. :)
(This was on Windows 7, using Indosat IM2 in Indonesia, but I think the same solution will work for other systems and providers as well.)