Remove old iMac from network?
I'll hazard a guess that the connection to your old iMac is one you set up on your new iMac. Here are some places to look, if this isn't it, please let us know: 


Look in Control Panel, the Users &amp; Groups item, the tab labeled Login items. Is there a reference in there to a folder or anything to do with the old iMac? 
In Control Panel, the Sharing item. Open this, and look for anything shared with your old iMac. 


Hopefully, it will be one of these, but if not, perhaps edit your question to provide a bit more information. It's difficult to say what information exactly, but an example would be if you used the old iMac as a network connection, used VNC to connect to it, etc.