Does the ActionTec by any chance have an option to force a specific wireless mode, such as wireless G or Wireless B instead of the typical Mixed Mode they are set to by default? You'll find such options often times under the Advanced Wireless Settings. Try forcing it to use Wireless G to see if it will connect. If not, I would have to say it's possible there's an incompatibility between the Roku's Radio and the ActionTec radio.
If your old ActionTec is still working, you're free to put it back in service and keep the newer ActionTec as a spare should your old ActionTec router die on you. If that isn't an option, you can see if one of Verizon's Westell 7500s may work, or you can try setting up another wireless router as an access point if you have that option. Otherwise, if you absolutely cannot get any wireless solution working, you could look into getting either a MoCa connection or an Ethernet over Powerline solution set up so that the Roku will work over an Ethernet connection. That's obviously a last ditch effort from the sounds of things.
Good to hear some progress was made. If you log into the ActionTec again and look around at the "Advanced" section, do you see a Firmware Upgrade option? See if you can upgrade the modem firmware via the modem's interface. If that doesn't work, I'll see if I can locate a link for your modem.
I am not a verizon customer but experienced the same issue with my GT704WG and rokus. Actually it was also a problem with my vizio tv running netflix. The problem seems to be that the netflix devices don't play nice with the actiontec router when the dns servers are hardcoded in the router setup. Once I told the router to get them from the isp the rokus could function properly, however, the old roku worked flawlessly and the new high def xd/s occassionally lost track of the router and I had to flip the router power off and on to get the roku to see it again. This usually happened a couple times a week.
I did finally cure that problem, and a few others, completely by installing openWRT on the router, but it was like pulling teeth to get the wireless set up correctly. If you are linux friendly, or a massochist, you can try openWRT, it offers more control than any firmware supplied by actiontec or verizon or quest, but it's no picnic to install and get running on the actiontec. You can get a version of openWRT with a gui from x-wrt if you go that route.
Let me say one more time though, I am a linux user and it still took me the better part of 2 days to get that running and configured properly.
My Roku will not connect to the internet. I have a Verizon GT704-WGB. The Roku worked fine with my older Belkin and modem.
With help by Roku support and Verizon support , I have changed the channel, I changed the DNS I also changed the DMZ . The DMZ made the Roku work for half a day.
By reading your comment I should bought another Belkin instead of going with the GT704.... It sounds to difficult to go the route of , installing openWRT on the router.