OK - I heard back from my web admin (they rock!) - here was his response:
"the problem may be caused by mod_security . It seems there may be a security hole in xmlrpc.php so the firewall is telling the pinging machine "file not found". What version of xml-rpc and or WordPress are you running?"
I have yet to hear back from him (because I just now responded to his question) but hopefully he might have some more insight into this later on ... All this is well beyond my knowledge, so at this point all I can do is relay messages and follow instructions, but if anyone has any ideas about this, it would be much apprecaited ... (and, for the record, I'm using the latest version of WP, but as I've said before, I've tried everything from the CVS version to 1.5 alpha - and yes, I have been deleting the files before moving the new ones to the server).