Welcome to the Community,
pinging the Windows 7 may be blocked by the Windows firewall. Anyway, you should be able to reach the Internet with either Bridged or NAT networking. How did you configure the network settings in the Ubuntu guest? Is it configured as DHCP client? In case of Bridged you should get a lease from a physical DHCP server (e.g. your Internet router) and in case of NAT the VMware Player DHCP service will provide the lease.
André