Can you browse the other computer from Firefox?
Or can you just see it?
You should have the same workgroup name and I think password in both computers
I think XP defaults to "Workgroup" (and please note that the case of letters are important) and you should make the Mint computer member of the same workgroup
Here's the link
to a howto for Samba
Use Advanced Search to search for samba or most any networking thing and the user miket
He is by far the most knowledgeable person in the forum but has turned to farming in France so he is not here very often any more