The majority of problems in Windows XP Home come from the inability to easily change security permissions. In general, windows will attempt to first connect to a remote computer using the local credentials. When that fails (because the remote machine doesn't have that user account) it defaults to the "guest" account. By default, this account is disabled and has the "Deny access to this computer from network" security policy applied to the account. This is mainly used to "protect" the user from unauthorized access. Which in reality, doesn't keep anyone safe and just causes problems when you want to share files.
Now simple file sharing is supposed to manage all of this stuff for you, but it doesn't always work. So before you go hunting around, check out the following site, see if the steps included allow you to connect:
If you've done everything explained in the above links, it's time to dig into the OS utilities.
The first thing to check is your user accounts. My favorite way to check this is to Right click on "my computer" and go to "manage". Under "System tools> Local Users and Groups> Users" it should show you all users on your computer. There are two things you can try, enable the guest account, or add the user account that is used on the non-XP machine. If you create a user account that uses the same password that is used on remote machines, it should use that account instead of the guest account when connecting to your computer.
Once you have verified that your guest account is enabled, check on the security settings. Go to "Control Panel> Administrative Tools> Local Security Policy". Once in the utility, go to "Local Policy> User Rights Assignments" and find "Deny access to this computer from network". Double left click the item to modify and remove Guest. Hit OK and close out the utility. You should be able to connect to your shares from the remote machine.
I am 99% sure that you have access to both of these utilities in XP Home, my one XP Home machine was setup a few years back and I haven't messed with this recently. Though every time I setup an XP machine at all, I have to do this process.
Hope this helps