Can’t access files on Win XP Workgroup

I have a home network of 2 Windows XP Professional computers. They are connected through a Linksys Cable/DSL router. The 2 computers are able to see each other but I am not able to access the files on either computer from the other. I receive the message “\\Computername is not accessible. You might not have permission to use this network resource. Contact the administrator of this server to find out if you have access permissions. Logon failure: the user has not been granted the requested logon type at this computer.”

Please let me know what I can try.
Thank you.