So call their bluff. Unless you're dealing with the support for some small/fly-by-night company, phone support is going to have someone overseeing them. If they absolutely refuse to connect you, hang up and get a new agent and ask to speak to the supervisor from there. Make sure to provide the supervisor with the calling agents details.
All of them have a supervisor or superiors of some sort. But in some companies they do not touch the phone, they overseer the process. I can tell you from personal experience that if the customer support doesn't solve the problem then there isn't a next "level" of support called the supervisor, but only more formal options to communicate remain; think complaint department, mail, lawyers.
