All these error codes are the ones coming from Windows itself; the server's code to do remote client installs calls windows APIs such as WNetAddConnection2() to do its work, and in situations like this where the error numbers coming back from the Windows API make no sense to us, we just report them.
Error 10 has something to do with Simple File Sharing which is turned on by default in Windows XP and makes the APIs we use just fail until it's turned off by hand in Windows (from any Explorer window under "Tools", "Folder Options...", "View" tab, at the bottom of the list of options) on the client machines.
For the other errors, one possibility is to do with whether the client machines are part of a domain or not. The way the network subsystem in windows deals with a name like "User" is completely different depending on the domain memberships of the two systems, because NT machines not in a domain tend to think of themselves as the center of the universe, while machines in a domain think of a domain as the center of the universe. If you don't specify a domain part of the username (e.g. "MyDomain\User"), workstation machines tend to just assume you meant their own name and things actually work pretty well. However, domain machines tend not to assume anything at all, and they like to insist that you explicitly say what domain a user is part of.
Turn off simple file sharing, and experiment with explicitly qualifying the user name that you use you connect to the client machines, and let us know if you make any more progress.