Quote Originally Posted by caravel
Hmmm... try manually entering the DNS servers on the desktop and then for the primary DNS of the laptop enter 192.168.0.1 and nothing for the secondary. Reboot, then try again.
Desktop's internet connection was automatically obtaining an IP and DNS address. I left the IP automatic, but manually entered the 2 DNS addresses. I then entered the gateway and primary DNS for the laptop as 192.168.0.1. Tried IE on laptop, failed, rebooted laptop. Tried laptop IE again, failed, rebooted desktop. Tried laptop IE again, failed, rebooted laptop. Tried laptop IE again, failed. Throughout this, the filesharing has been working OK, and the desktop can connect to the internet.

So basically the laptop can't connect to a DNS, for whatever reason.