As a receptionist how do you nicely handle certain phone calls?

At my company all I can do for people is get some basic information from them and I will know where to send their call. Just their name, who they work for, if they have an account with us or not. Then I can get them to the right person to help them. Often I get a call from someone who goes directly into their problem like I am the know everything person, talks so fast and won't let me even get a word in to ask them the basics I need to send their call to the right office. Like some people go into a life story. When I quietly listen they finally wind down then get angry when I have to ask for the basic information I need to route the call. In the meantime the phones are backing up and others have to wait. How do you nicely handle these calls? I enjoy my job as answering phones is one of many parts I may do that day and I want to help them but they don't let me ! What can I do ?