To see whether this is a host OS issue, try to ping the Win7 Client from another system on the network.
Regarding the guest. With NAT configured, what did you try to ping? The host's virtual NAT adapter's (vmnet8) IP address or its physical IP address?
In case of Bridged, open the Virtual Network Editor and try to select the connected NIC for the Bridged network from the drop-down list, rather than "Automatic" to see whether this helps.
André