first off, if you cannot see both computers in network neighborhood, that's ok, windows is buggy for that. Make sure both computers have TCP/IP and both use the same Primary Network Logon (in the Network properties). If still don't see all computers in nethood, forget it, it's not that important.
now, about your internet connection.
if you got the WAP11, it does not have the internet sharing function built-in.
to have built-in internet sharing, you could either add a BEFSR11, or exchange your WAP11 for a BEFW11S4.
If you want sharing without getting either of those, you could use Microsoft's Internet Connection Sharing, which comes with Windows ME. Or buy a third party program that do similar things. However, with either of these software, you need to dedicate one computer as the server, and the other can only get internet connection from the server when it's turned on.
There might be a third option, if your DSL provider has it available. Which is buying another account thru the same DSL modem. It costs a little more per month, but you don't need to share the internet connection, just share the modem.