That 22.214.171.124 would be your nameserver?
It should be the same as in your windows config.
Also, I'd expect the directive to be "nameserver 126.96.36.199", rather than just the address, but I'm on CentOS. Also, I'm missing the default search domain. But as you state you can ping websites by name it may be OK. Also, normally you'd use your local DSL gateway address as your nameserver, and I would not expect 188.8.131.52 to be an address on your local lan, as it's not in a private IP range. The address you use is part of InterNAP Network Services's network.
Here's my /etc/resolv.conf:
$ cat /etc/resolv.conf
; generated by /sbin/dhclient-script
10.10.1.254 is my DSL gateway.
What do you mean by 'hit my network gateway'? Can you open its config in your browser? Or just ping it? What's the error you get when trying to browse to google.com? 'not found' or 'not responding'.
You may also want to check out Windows Firewall, or whatever firewall you're using on Windows, to ensure it's not blocking you VM's traffic.
Please post back with specific action details (i.e. not use terms like 'hit') and exact message information.