Lose internet when plugging into switch

Question

I am perplexed why I can create a wireless network with my airport extreme and have great internet connectivity through my cable company, but when I plug the airport into a switch to distribute the internet through out my office the internet immediately starts slowing down and eventually completely goes away.  Unplug extreme from switch and the internet comes back for wireless clients.  Problem started about a month ago.  I figured switches were going bad so I replaced every switch in the office.  Did not solve problem. Thought maybe airport extreme was going bad so I replaced it  with latest  airport extreme (cube). Problem still exists.   Nothing has changed in my network configuration in past two years.  No other services that use the network is effected, just internet connectivity.  I was quite ugly with my internet provider thinking it was a service issue until on a whim I unplugged extreme from switch and my iPad, iPhone, and macbook pro were able to connect to the internet wirelessly instantly.  Plug it back into the switch and internet connectivity for wireless and wired goes away.
Any suggestions are greatly appreciated.

Answer 1

That's only one explanation, and an oversimplified one at that. In any event I think your best course of action might still require disassembling your network and adding one piece at a time. Assuming your business is closed for the weekend, now might be your best opportunity.
Short of that, power down all switches, Macs, other devices (though I doubt iPhones, voip phones or printers can contribute to the problem) and the Extreme (no need to reset it). Then, power up the Extreme and one Mac that is connected through a switch. Turn Wi-Fi "off" to ensure Ethernet is its only viable network connection, as well as for troubleshooting simplicity.
It should have no connection until you power up that switch. Do that, and determine if the problem still exists.
Assuming it doesn't, turn its Wi-Fi back "on" and test.
The iPhones and iPads should also be working at this point.
Proceed to the next Mac and test the same way. If it's connected to a different switch, power it on also, then re-check the first Mac.