Bought a brand new iMac and the and the internet is running very slow

Without much information it is almost impossible to help you. What exactly do you mean by " the internet is running very slow" Does that mean you e-mail is slow, surfing we pages is slow etc.... Without being specific we have no real idea what you are talking about. We rely on your to draw a complete picture with words, without that we are left guessing.

However where I would start is by telling us how the computer is connected to the Internet, do you use wi-fi or ethernet, what speed is your ISP telling you you should be getting, have you done any basics like resetting the router and modem??? Please answer all these questions and describe the condition and then we can starting helping.

Well you have 90 days of free AppleCare telephone support. Time to call them. You did not read my first post in full and did not provide any information other than your ISP and that you have another iMac that is working okay. You ignored my other questions. AppleCare should be able to give you a hand.