Both sides of the link need to be compatible so perhaps the Wi-Fi card
in this Ubuntu system doesn't have WPA or doesn't do it as the router
is expecting. Seen that sort of thing myself when an adapter that
*should* have been WPA compatible don't get on with WPA routers !!
Only way around it is to use a different Wi-Fi adapter or different
Router.

FWIW - if you are in a remote location then WEP is probably enough but
in a suburban or city environment it really is 'open house' for anyone
so you'd need other security options like MAC address filtering or
even severely restricting the DHCP range of addresses - if you only
allow one address then when you are connected the DHCP server will not
be allowed to provide another address for anyone trying to piggy-back
your Wi-Fi