See if you can figure this one! Brand new wireless router works then stops working

Here's the really wierd situation in brief.

We just moved into a new house. I have a cable internet coming into a modem and am connecting a wireless router to the modem. Modem works fine, I've tested it connecting to my laptops, great internet.

I connected my netgear wireless router to the modem (same configuration as prior house), it doesn't work. I can see AND connect to the wireless router, but NO internet.

After spending 90 minutes with tech support I give up and just go buy a new router. $40 later I've connected it to the modem, run the setup and it works like a charm. I connect my first laptop and my ipad to it, internet running smooth.

Fifteen minutes or so later I try to connect my second laptop to the wireless router. SAME PROBLEM as with the old router...connects but NO internet. In addition, the ipad and first laptop which both worked fine after I installed the new router, stopped working as well. All devices can connect to my neighbors wireless with no problem so it's something with the router i would think...but why would it work then stop? Same problem as the prior router.

What is going on???