Just bs and say you're having some connection problem and ask them to reset your IP "to see if it fixes it".
~
changing/getting a router wont change external IP address btw.
I also think we're having the misunderstanding that Static means it can not be changed. The term static IP strictly refers to the fact it doesn't change everytime you get online as was the case with dial-up. Even if you're using DSL/Cable DSL your IP can be bound to change every once in a while, due to you ISP tinkering with its server.