Welcome to this community.
Few suggestion.
1. Is the Virtual machine with windows is able to ping outside from you client machie or you able to take RDP of that window machine.
2. Is firewall is OFF and network discoveru is ON in the windows 2008 virtual machine.
3. Is the windows virtual machine resolve DNS.
4. Could please check on the ESXi host is that able to ping to any internet site like ping www.google.com
5. Is that the VM is in same VLAN as other machine where the internet is working.
6. Did you check is the proxy setting is same in the virtual machine and other machine hte network with working internet.
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