Xbox one won't let me sign in yet controller works.

this may seem weird, but can you try with a different controller?

sometimes one of my controllers refuses to let me sign in or access the Xbox menus yet my other controller has no issues.

Same here. New Xbox One and can't do anything without first signing in but won't let me sign in but web site works fine.

I am playing on Xbox one it won't let me sign into my profile so I removed it now it won't let me download it

That's strange indeed as if your network connection may possibly be blocking the websites.

Try to use a different network connection/Internet Service Provider as part of our troubleshooting steps.

You may try to access your account on your friend's home network on Xbox.com and account.xbox.com.

Yes, that is accurate. It seems I am able to log on to my console.