Correct. However, I resolved the issue, although I didn't exactly find the problem.
I guess I made the mistake of modifying my DHCP to point to the DNS server BEFORE I set up the DNS server. So all of the machines that had already connected via DHCP were having trouble reaching DNS.
I expired all of the DHCP leases, and they started connecting. Clearly not a VMware issue at all, so I apologize for taking up the time in this forum.