I have a Debian Linux with Eth2 set up to Bridge with my network. I can ping my gateway 192.168.1.1 and my host 192.168.1.4 as well as access the gateways admin page but I can't ping the internet. My /etc/resolv.conf says 192.168.1.1 is my DNS server.

I set it up with a static IP address and tried DHCP but I still cannot access the internet, I pinged google.com by its hostname and IP but it gives destination host unreachable.

My Host and Guest machines both have no firewalls running.

Any idea why I can't access the internet?

I had a similar issue with OpenSuse as VmWare guest.
Oddly enough, I had chosen the wrong driver for the guests ethernet card!
Some way this made it impossible to reach internet, but local network worked fine.

Use dig or nslookup to test resolver.

Ping is a poor test more and more.

As a rule I use NAT to set up VM's. A NAT uses a virtual router but you'd still have to apply DNS ip addresses. Better to use two or more. At least use the one assigned by your isp and even a common open one.