Some NAT problems are subtle and don't appear in the Test Xbox Live Connection test.
Most likely there's a port blocked... ports can be blocked in your router, modem, or at your ISP. Since the Xbox 360 uses different ports than PCs & Macs use, you can't see the effect of a port blockage except on the Xbox.
A sequential power cycle is the first step in clearing a port blockage:
1) turn off the Xbox then
2) unplug the power from the router .
3) unplug the power from the modem.
4) Wait at least 30 secs then replug the modem (power.
5) Wait 'til the light on the front of the modem which says ONLINE, READY, CABLE or DSL is on solid (not flashing), then plug in the router.
6) Wait one minute or until the WiFi light on the router is on, whiched comes first; you may not use WiFi, but it's still a good indicator your router is finished booting up.
7) Turn on the Xbox. For more background on Ports, see whatismyipaddress.com/port