I don't know if the iMac can "crash" the ENTIRE network. Maybe it can, I don't know/ Try Apple again and tell them everything that is happening. Keep them on the phone while they suggest things and when they dont work, tell them. Do you have a warranty or insurance?
this happened to me on my macbook, only would happen on my schools network, but now its fine, but I used to ping yahoo.com in terminal and that sometimes helped