I hear you... I went through this with TWC in late 2007 and it took me a month of repeated calls and truck rolls to finally get it fixed. Finally a tech found a bad connection in a junction box a couple miles away and it has been fine ever since.
Just to save you some hoop jumping on the phone, take the router out of the picture and connect the iMac over ethernet directly to the cable modem, then reboot the cable modem and test that way. That is what they will make you do over the phone. This will prove to them it is not your router.
Seems like my wife's laptop connects great and when I connect to iMac we get kicked off wifi so I tried what you suggested.
I connected my iMac with Ethernet cable directly to the sb6141 and it was very slow connecting to website. At least a minute.
I connected my wife's laptop to Ethernet cable and it connected right away.
What could be causing the issue with the iMac not connecting