This assumes that you have a network connection but cannot get the Xbox Live to work on the Xbox 360.
1. Reserve a static IP address in the DHCP range for the router (verified by MAC Address).
2. WAN: Internet Connections: Basic Config: Enable PNP: NO (Apply change)
3. WAN: Virtual Server/Port Fowarding: Enable Port Forwarding: Click on YES (Apply change) - Note that there is no need to make any other changes in this section for purposes of using Xbox Live.
4. LAN: Switch Control: NAT Acceleration: Select DISABLE (Apply change)
5. Click the "Reboot" button at the top of the menu page to reboot the router.
6. After the router has rebooted, go to WAN: Internet Connections: Basic Config: Enable PNP: YES (Apply change)
7. Click the "Reboot" button at the top of the menu page to reboot the router.
8. Turn on Xbox 360 go to "Network Settings" and apply factory default settings. The Xbox 360 will then select your Reserved IP address and Gateway information automatically.
9. Test and verify that Xbox Live connects properly.
10. To check that the correct ports are working on your Asus Router from the menu - System Log: Port Forwarding: Click Refresh You should see the IP address you are using for your Xbox 360 using port 3074.
I have Comcast IPv6 in our area and have that enabled. I believe the Xbox One uses IPv6 which might be why I can use both the Xbox 360 and Xbox One simultaneously. Those with IPv4 only may not necessarily have similar luck.
As a side note, I use Merlin Firmware 22.214.171.124.374.40 Alpha 4 firmware which is based on Asus' own firmware though it has a lot of improvements. Search for Merlin ASUS Firmware to find it. I believe Merlin actually helps ASUS identify issues and helps them with fixes on their routers.