I have a laptop connected to a wireless router, the desktop wired to the same router but when I try to access the web with both at the same time, the desktop's IE session is disconnected and I can only reconnect by shutting down that session and starting a whole new IE session. Is there some setting I can make so they all play along nicely in the same sandbox?

Sounds like an address conflict.
Do they have different addresses?

Go Start > Run and enter cmd then OK to bring up a command prompt. Type in ipconfig then enter, the result will show the assigned IP Address. Make sure both pc's have different IP Address's.

I don't think they have the same address, if they did have the same address you should be getting a message popup saying there is an IP conflict. The popup should show before you ever get around to bringing up internet explorer. The connection is made regardless of IE running or not, email and other apps use the IP connection as well.

They have different IP addresses (only different by 1 digit). They seem to be working at the same time with no problems now. Before, when it was happening, the laptop was trying to do a Windows update of some sort. Seems fine now.