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Given you have Modem==Router(wifi-g) and the router doesn't support N mode, you need a second router.
Setup the new WiFi-N router to
Now cable WiFi-g(lan port) with rj45 cable to WiFi-N(lan port) and leave WiFi-N WAN port empty.
WiFi-g will provide all DHCP services for both G/N wifi connections
as well as all wired connections (regardless of where connected).
Connections to the -N ssid will use the N mode settings
Swapping out your cable modem can be a problem. I found this out with Comcast - every time I wanted to make a change to my home network, or performed a reset, I'd have to call up Comcast to get "re-authorized". Sometimes they would change the DHCP address assigned to my modem, then I'd have to call them again to get re-authorized. In the end, I would have been happier just sticking with their stupid Wifi G.