It sounds like you have a connection. There are a couple of things to test.
1) on the axim WLAN settings -> Network Adapters -> Dell Axim Wireless Connection You should have Use server-assigned IP address
2) When connected on the Axim in WLAN under Advanced see if you have an IP address, gateway, and Net Mask. The IP will be assigned by the router, the gateway will be the routers IP address, and 255.255.255.0 should be the net mask.
3) On the Router trun off wep - security can be added once the connection is working. I don't use web because there is nobody within my transmit range that could be watching my net trafic.
4) On the router check for attached devices. your axim's name and mac address should show up there. If it is not on the list then. On the router turn off Wireless Card Access Control. Then try to connect with your axim. If it appears now add the axim to the wireless card access list then check turn access control on. This will keep your router from being a public hotspot.
5)On the axim if you have an IP address on in the advanced tab then go to the tools tab. Press the Renew IP and the IP should stay.
5.1) Ping Yourself - enter the AXim's IP address in the box next to the start button and press start. You should get replys. If you don't go back and set up the "card"
5.2) Ping the router - enter the gateway IP address. you should get replys. It is posible to configure most routers to ignore Pings, so if you don't get a reply then check that setting.
5.3) Ping an internet site. try 209.215.97.173 that is the IP for
www.aximsite.com. You should get replys, I just did. If you do then you can reach the internet but your DNS is not working. This is where the proxy thing always gets me. I have a friend who gets the same problem but he fixes his by turning something off in Odyssy. He could not tell me what.