Xbox 360 can connect to Internet but cannot connect to Xbox live

I have the same issue. Suddenly I was disconnected from Live and I could never connect anymore. The XBOX 360 can connect to the router, but cannot access to internet. I tried with another WiFi but it's the same.

Hello

Status code: 80004005

Some connection types and Internet service providers (ISPs) cannot access Xbox LIVE Marketplace from the Xbox 360 console. We are aware of this problem and we are working with ISPs to resolve the problem.

Solution: Use a different Internet connection

Connect your Xbox 360 console to the Internet at another location using a different ISP. For example, take the console to a friend’s house and connect to the Internet there.

Ive continued testing things to try and get my xbox connected and still no success.

It always connects to the internet, but refuses to connect to live.

It says "Your console is connected to the internet but cannot contact xbox live."

So would this mean its something on the xbox live servers side?

I know my ISP isnt blocking it since I already called and they actually tested an xbox 360 themselves to try and check, and they could connect.

The first two days that this was happening to me it would connect to the network, it would connect to the internet, then not to Xbox Live. Since then, however, eight days have passed and I'm on the tenth day of no Xbox Live and It continually says that it
can connect to the Network and Router but cannot connect to the internet and gives me an MTU error.

I tried again last night and my 360 automatically started an update, the issue is now fixed. I am glad that they either decided to address the problem, or it got fixed by dumb luck.