Hello awlsew

                      G34 is a gateway combination of modem and router so for this when you connect the separate router to the modem you need to enable bridge mode on the modem so the wifi will be disabled, so please follow the steps mentioned on the link below to enable bridge mode on G34

                   http://arris.force.com/consumers/articles/General_FAQs/G34-G36-Bridge-Mode-Setup

Let us know if this helps

Will all the ethernet ports work in bridge mode? I am needing to hard wire one device separately from my wifi.

No it won’t. Bridge mode turns it into a modem only device and only 1 device can be connected to it (for most isp’s). 

Why not leave it in router mode and put the router connected to it in access point mode? 

Yes, I am wanting to leave it in router mode. I just want all the wifi turned off of my G34 making it an ethernet only router using two ports.

One port for a hardwired computer and one for a wifi router.