My desktop has been shut down. But my modem and router are still on.
Should not my laptop still be able to connect to the internet? thanks.

How are they all connected? If the laptop is attached straight to the router, then they should. If the desktop is being used to share the connection, then the connection won't be available to the laptop without the desktop.

Tacit,
thanks,

Yeah, the desktop does not share anything. The laptop is in the other room. So then why does the laptop, which resides in the other room, unable to connect when I shut down desktop.

PS, my last email PM, bounced back, you normal email is not working anymore?

Hmm. If the laptop is connecting to the router directly, the desktop should make no difference to the equation at all. I assume the router is appearing in your AirPort menu?

I've been told by a few people that email to me is bouncing intermittently. I have a few other emails that don't run through AOL, like franklin (at) xeromag (dot) com, that might be more reliable.

Tacit, thanks, no the laptop is not touching the router.
Only desktop is plugged into the router.

Does the laptop have a wireless network card? Is it a wireless router?