That's strange. From your first post it looks like the "VMware NAT" and "VMware DHCP" services are working (please double check in services.msc), since you received an automatic IP address in the guest OS and you're able to ping the hardware router. However, something seems to be blocking communication. Do you have any kind of Firewall or Endpoint Protection software running on the host, in which you may need to allow the virtual NAT network adapter to communicate?
You may as well want to check the Windows Event logs for errors/warnings.
André