Ideas, please?

I'm hoping that someone out there can give me some ideas about what might be going on with my home network so that I will know which tech support to call and won't look like a total goofus when I do. 

First, you must promise not to laugh at my lack of tech-savvy. Yeah, I have a blog. That means nothing thanks to the Blogger wizards. And I use a Mac, which means I really don't have a "need to know."

I have a DSL/broadband modem, courtesy of Verizon and use an Airport Extreme base station for wireless. 

My computer shows that I am connected with a lovely signal.  All the lights shine correctly on both modem and router.  

But I can't connect to the 'net.  Random sessions of restarting, fidgeting, unplugging/replugging everything will reestablish connection for a few hours, then nothing.

I've been crouching in the corner of the upstairs guest room swiping my neighbor's signal for weeks now. Tonight I finally dug out the Sprint USB modem I use in Oregon and installed it on the new Miss Mac so I can roam freely 'round the abode.

So, my technical superiors, do you think the problem lies in the modem or the router? Do I call Verizon or Apple? Do I disconnect with Verizon altogether and  just use the USB modem since I'm paying through the wazoo for it, anyway? But if I do that, then I can't buy the groovy new Time Machine I have my eye on.

I'm hoping for a veritable storm of comments.