I've got Windows XP Pro running on a system with simple file sharing turned off. I've tried to set up a local account on the system, but, when I try to open the network share it simply tells me access is denied instead of prompting me for a username.

My question is, then - can I set up the server so that it uses an account local to my client machine OR be prompted with a login so that I can use credentials local to the server? If so, how?

You probably have the guest account enabled but gave it no rights to the share, resulting in the access denied message. You either need to give the guest account (on the hosting pc) rights, or disable it.