Recently I bought an Elite (or that said the serial number when I added it to my Microsoft account) Xbox 360 from second hand and I'm trying to connect it to Xbox Live to download free TV app (from spanish public TV) and some games from microsoft web.

I have my own profile, and the console is connected to the router. It doesn't say the usual "If you don't connect you won't be able to save" that says when it's on my room without Wi-Fi, so I guess it is connected to internet, in addition to the connection trials from the settings. I have the avatar in the main page also.

But, when I access the shop, for buying, for example, GTA 5, it says that I must connect my Xbox Live account.

Creating one gives error saying that the password isn't correct (how could that happen if it's new) and trying to use my Microsoft account doesn't work (even when Google save it as live.com user and password). When I select the other option, it sends me to the profile selector.

Microsoft has joined the Xbox to my account through serial number, and I have the Xbox app for Android.

What should I do? Thanks in advance for the help.