What is the ruling on a conditional divorce pronounced in the form "If you speak to so-and-so, you are divorced," if the wife presses the phone buttons without completing the number, or if she calls and the line is busy or rings without an answer? Does this include calling via the internet?

The preponderant view is that a conditional divorce takes effect upon the fulfillment of the condition, regardless of the husband's intention. The determinant in defining the condition is the husband's intention behind what he uttered. As long as you intended to prevent your wife from telephoning these two individuals, then you have broken your oath by that act and nothing else. The oath is not broken merely by her attempting to call without speaking. If you are preventing her from contacting foreign men (non-mahram (definition)), then it is obligatory for her to obey you, and it is not permissible for her to contact them by any means. Her threatening you to do so is an act of disobedience. You must prevent her from forbidden acts through admonition, then by abandoning her (in bed), then by striking her without causing injury, and not by threatening divorce.