OK, this is one of those summaries that I really don't want to post, because it just points out my lack of knowledge.  Thank you to all who responded--but a BIG thank you to Ashley Frost who helped me figure out that I'm an idiot. ;-)
It turns out there was never a problem with the DNS server at all.  What I did was ping the new Online server from the DNS server, and it timed out BECAUSE it still had the old address in the LOCAL host file.  I never tried Pinging from another server (if I had I would have seen perfect connectivity).  So there is still a problem, but it must be an XIPC or Informix thing...which isn't really my department.  Thanks again to all, and sorry to have wasted your time.  
-Jonathan Williams
Received on Thu Feb 15 2001 - 21:48:41 NZDT