Obviously, you do not have access to the internet from your Linux machine.

First I would find out if I can access the internet from the host machine.
If I can, then I will verify my network settings on Linux. Otherwise I would trouble shoot the internet access for the host first.

Issue this command on Linux as root
/usr/sbin/system-config-network

See if Linux is getting an IP address from the router.
Make the IP address static if you can.
Copy paste the screen shot of your eth0 settings, if the problem persists.