Xbox Live [Issues signing into Xbox Live on Xbox 360]

Currently there is an issue signing in to Xbox Live on the 360. Please be patient and keep an eye on the following status link.

support.xbox.com/xbox-live-status

There appears to be an issue with Xbox Live on 360. Here’s a thread: Xbox 360 cannot connect to Live

Xbox 360 doesn't use Azure servers, it uses 15,000 Xbox Live servers. It's the Xbox 1 which uses Azure servers, 300,000 Xbox Live Azure servers.

This new issue affects only the Xbox 360. See my earlier post details. This issue IS Microsoft's issue. When you are not signed in, you can bypass the black screen by inserting a game disc of the game you want to play, the Xbox 360 Dashboard loads that fine,
while it's doing that, sign in. It worked for when I wanted to play COD BO2. But when I start my console and sign in then, launch an app or game, I get the black screen. It's not a defect of the Xbox 360 Dashboard. It's the *source" which Xbox 360 is connected
to, and the only service which Xbox 360 consoles are connected to, is one thing only, Xbox Live.

Just using the Xbox 360 and am unable to connect to Xbox Live. According to Down Detector for Xbox Live, there seems to be plenty of other similar reports. There's even an alert on the Xbox.com service status page about signing into Xbox Live https://support.xbox.com/en-US/xbox-live-status
That page also includes signing into Xbox Live on an Xbox One, but sometimes the issues don't seem to effect everyone the same way.

Sorry to hear you're having issues. Currently there is a problem with signing into Live on the 360. Support is aware of the issue and are working on fixing it as quickly as possible.

support.xbox.com/xbox-live-status