I think something isn't being understood here. The ideal setup is:
cable -> Actiontec 424 -> ethernet cable -> DIR-825 -> your devices wired/wireless
This can be achieved whether or not the 424 supports bridging or not. I've spend a while tonight reading the Verizon manual for the 424 and looking at other forums to really get an idea of what this thing does. I do realize the signal is delivered to your modem via coax instead of fiber or ethernet--which is to be expected unless you were wired up in a new home.
Most of what I'm reading indicates you'd need a very intimate knowledge of the 424, FIOS, your particular wiring setup, the 825, and networking.
So to help keep it simple:
On the 424, disable the onboard wireless completely (See this link:
http://www.smallnetbuilder.com/images/stories/lansrouters/actiontec_mi424wr/actiontec_mi424wr_wireless_big.png). Make sure the 424 still works fine with one wired computer before you proceed. Look for the DHCP settings and take note of the range the 424 will assign (See this link:
http://www.smallnetbuilder.com/images/stories/lansrouters/actiontec_mi424wr/actiontec_mi424wr_advanced_big.png and go to IP Address Distribution) - if the start and end range goes from 2-254, reduce/change it to 2-100.
Connect one computer and nothing else to the 825. Go to manual network setup and disable DHCP. Also, assign the 825 an IP address that is OUTSIDE of the DHCP range of the 424 (i.e. if the 414 assigns 192.168.1.2-192.168.1.100, then choose one that's NOT in that range, such as 192.168.1.120). Make sure you SAVE before stepping off network setup. Then go to manual wireless setup and set it up the way you want in terms of SSID, Security, Wireless Mode, etc. When you're done, make sure you've saved again.
Now, connect port 1 of the 424 to port 1 of the 825.
Test the wireless and see if you can get on the net. If that fails, test it by connecting it WIRED to the 825 and see if it works again. If it still fails, double-check the steps I outlined. Missing one step will break everything.