iMac causing recurrent internet problems

A couple of weeks ago, we started experiencing recurrent problems with extremely sluggish internet speed (we are on Internet 18 plan). We had one AT&T technician come out, who checked for any service issues outside the house, and found no problems with service to the house. Then we had another technician come out who did troubleshooting inside the house. After checking all of the basics, he looked at the Diagnostics on the BGW210 router's setup page. He ran some tests with turning various connected devices off and on, and said that he thought that the problem was related to one of our desktop computers. But after we restarted all devices, the problem disappeared and everything was back to normal, of course.

But today the problem is worse than ever. I have narrowed the problem down to the iMac we purchased a few months ago. Everything will be working fine with the internet, then come grinding to a halt. I then disconnect the iMac from the BGW210, and the internet almost immediately comes back to normal on all other devices (a second desktop Mac Mini, two iPhones, two iPads, and one Apple TV). I reconnect the iMac, and things may be fine for awhile, but then the problem recurs. It does not matter whether I connect the iMac via Ethernet or wireless connection.

Here is info I am seeing in the Diagnostics when there are problems:

Under Diagnostics -- Ping Default Gateway = Fail

Under Logs -- There are seemingly random sporadic "Other DoS Attack" events, with various DestinationIP addresses matching IPv6 addresses of our devices. Sometimes it is the address of one of the iPhones, or the iMac, or the AppleTV. The timing of these events seems to correspond roughly with the timing of service issues, but that is not at all consistent.

Anybody have an idea what is going on and how to fix it?

Thanks.