live won't work on my 360

You might want to check your Services and Subscription tab to make sure the Live has been activated on your account.

Did you just add the gold to your account? Try testing your neywork connection. That should resync the console to Live in order to make sure everything is updated.

If the issue persist, may i know if your current password has more than 12 characters?

stalker status

Hi and thanks for reaching Microsoft Xbox gamer's community. My name is Josef.
I'm an Independent Advisor and a Microsoft Xbox user like you.

Hope you're doing great today despite this Brandon

Do you have an active subscription in your account?
Please double check this here:
https://account.microsoft.com/services

If yes, this can be a bit odd but turn off temporarily the recurring billing and then try again

If the issue persist, may i know if your current password has more than 12 characters?
If yes, please change the password and try again

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If maybe the above doesn't work, go here: https://account.microsoft.com/security with the account that you want to use on Xbox 360

Then press advance security options and scroll down to the bottom
Are you able to see something like "app passwords"?

If not, please please enable 2 step verification
After that go here again https://account.microsoft.com/security > advanced security options and you should be able to see "app password" option now.

Now please press on "create new app password" then, write that password instead of the actual one in your console

When you try and download your profile on the 360 what does it say?

Your credentials are incorrect? in other words your password is incorrect?

Is it giving you any sort of error message?

Have you ever played online with that profile on the 360?

The 360s did not require you to have a MS account like the Ones do and you could have a local profile. If this is the case for your account then you would not be able to put your current MS account on that profile on the 360 you can put another one on there
and here is a link that will give you directions on how to do that.

Offline profile for 360s