Still nothing on the email front. (4 hours)
Attempted multiple connection tests. Deleted all corrupt data from my hard drive. Tried to download my profile without the hard drive inserted. All to no avail.
Also wiped caches, removed updates, reinstalled XBox Live updates (clearly the XBox can connect to the internet, then..)
Still unable to download my profile due to problems with my "Microsoft Account".
Can connect to live.com and sign in to XBox.com no problem. So my XBOX account is all good.
I've seen the error message so many times the fact Microsoft have used the word "Something's" in their error message infuriates me.