i'm connected to internet, but safari won't open any pages.

Welcome to the Apple Discussions.

While the iPad shows you are connected to a wireless network, have you entered the email account information?

Go to Settings > Mail and either pick one of the preloaded email account providers, or enter your own account. Incoming and outgoing account information such as POP or IMAP for incoming, user ids, passwords. You can also check to see the port is set correctly for each.

With Safari, go to Settings > Safari and turn AutoFill OFF if it is not already. Tap the URL field at the top and enter the URL for your preferred home page.

See if that helps.

I'm trying to use a Verizon Fios Actiontec wireless modem; my new laptop and my wife's new iPad seem to connect to the network, but it might as well be a sham connection -- no Web, no email, no iTunes, nada. I suspect some encryption glitch, but it's only a theory, and I have no idea of how to pursue it.

notfa,

I'm assuming you are using DHCP. What values for IP address, Subnet mask, router, dns do you see if you go into Settings->General->Network->wifi-> (arrow beside the current active wifi connection)?

Also, In safari on the iPad can you access your router config page (usually at http://192.168.0.1 or http://192.168.1.1), or does that fail too?

Those values indicate that you are not being assigned an IP address via DHCP

Things to check:
- make sure, for now, that MAC filters are not enabled on your router
- make sure DHCP is enabled on the router

You can also trying using a static IP instead of DHCP on the ipad:

-change to static ip
- set IP to for example 192.168.0.155
- subnet 255.255.255.0
- router 192.168.0.1
- dns 192.168.0.1

Depending on your router you may need to use 192.168.1 instead of 192.168.0 in the above addresses, but try 0 first