Are you sure your wireless router is configured correctly (can you use it with any other wireless devices, or with a PC plugged into one of the ports on the router)?
Does the connection icon on the Axim show that you are connected?
What are the properties listed in the Dell WLAN utility? Open this, click more info... Should list your ip, subnet, gateway, etc...
Do you have the router set up with DHCP (both acting as a dhcp server, and getting it's connection with dhcp)? What happens if you try to browse an ip address rather than a name (eg 207.46.245.156 rather than
www.microsoft.com)
Are you sure that your school web page is not "cached" from surfing it in the cradle - making it look like you have a connection when you really don't?