The Nokia E63 behaves a bit strange when you want to use the built-in web radio application via mobile internet (UMTS, GPRS) instead of WLAN. The access point list is not always the same list which you find under SystemSettingsConnectionAccess points.
In my case, the mobile data connection was never visible when using the web radio, but the WLAN access points always were.
So I simply duplicated a working WLAN access point and then edited the entry. Then I changed the settings to those of the UMTS connection. I didn’t copy the proxy settings, anyway it worked and this entry was visible in the internet radio app.