Can't Connect to Xbox Live, doesn't recognize my Wireless Key

I can't connect to xbox live it doesn't show my wireless network

GTA IV sign-in on xbox for windows live doesn't recognize my product key,, so I entered it on the xbox.com redeem code page where it was recognized The game is still asking for my product key and not accepting it saying it's invalid, so I cannot proceed
to game.

What Country/State/Province do you live in?

-Philippines

Router brand & model number

-CISCO LINKSYS CQN11J100488

If Wireless, are you using a white or black external adapter, or an internal (Xbox 360S) adapter?

-Internal Wi-fi adapter

Things you have tried:

I really can't connect. Because my xbox360 console can't recognize my router.

In order for me to connect, I have to do these steps:

-Play games for 15 minutes(so that i can continue with the procedure of connecting online)

-turn it off

-unplug my power cord for 10 seconds

-plug my power cord back in

-turn on my console

-and then im connected to xboxlive

I can only connect to xbox live or my xbox can only recognize my router if i do all these steps.

and for some reason, when i can't connect or when im not online, my kinect doesn't work and it takes a long time for my xbox360 to recognize my controllers! please help me.

No my console is not banned I tried it being wired and wireless but it doesn't connect it just says I can't connect to live

I'm having the same problem. I'm connected to Xbox Live, but it doesn't recognize my profile. Says my profile is not signed into Xbox Live.