That's not a very useful executive. At the point it has been proven to be outside of your control it is time to get the customer support team working with the client to help them talk to their ISP and provide as much information as possible so that they can tell the ISP what is wrong. This accomplishes the task of letting the client know that it is not related to your service. It also lets them know that even though it isn't your problem you are willing to help in any way you can.
If he/she just keeps yelling at a tech that can't solve the problem, you have a leadership problem that needs resolving.
Yelling is almost never useful, back when I was a manager or director I would let the executive know that we are working on it and let us do the job they pay us to do. I also found it helpful that if you are having a vendor issue, let the executive send an e-mail stating it is an urgent matter to your contact, this lets the executive be a hero and gives the vendor bargaining power to escalate the issue to their upper management.
During an incident the leadership should be maintaining calm so that the people doing the work are at their peak performance.