Each OS has it's own quirks and drawbacks. Windows ME is a strange creation. Confirmation provided.
File and Printer sharing must be enabled. If this is not enabled on ME, you won't be able to 'see' the ME PC from either itself or another via the Network Neighborhood browser (NetBIOS response). You should still be able to ping the IP address of the ME PC from your XP PC, but won't see it by the network browser. Also, if you don't log onto ME by the Client for MS Networks, (not the Windows Logon -- see your control panel, network icon), you won't be able to see yourself or other PC's, but will only get an error on the Network Neightborhood browser (does't display workgroup names or PC names -- just nothing). You can actually be in separate workgroups or domains and still have rights and access to PC's in other domains and workgroups, but being in the same workgroup helps out quite a bit.
If NetBIOS is disabled on either PC, the other PC won't be able to see the PC name with NetBIOS disabled. In the Network icon under the Configuration tab, the option "File and printer sharing for Microsoft Networks" should be installed. In this option under Properties, you should have Browse Master set to automatic, since usually the higher OS will be the browser master.
Simplify your situation: use only one network protocol, like TCP/IP and eliminate NetBEUI and IPX unless you need IPX for gaming speed. We're all assuming your IP addresses are correct on each PC (same network, same netmask) and that you can ping one PC via the other (using TCP/IP).
Sample IP addresses and netmask for both PC's (netmask must be the same):
PCME
172.30.10.10 IP address
255.255.255.0 IP netmask
PC98
172.30.10.11 IP address
255.255.255.0 IP netmask
That's all you need to do. Don't enter any WINS or DNS server addresses or Gateway addresses, either leave those blank or delete anything in them.