Good news!! I fixed it just now (timing right?). It seems that for some reason uplay was configured to "always start in offline mode" :s
I change it to online and it's working now. I have no idea how this setting was changed to offline mode as I haven't touched any uplay settings for months.
Before this problem my password wasn't working a few months ago so I think I have been hacked... Is there any advice other than changing my password again?
Anyways, if anyone in the future is reading this and is having the same problem, try to disable your firewall. If it works, add ubisoft and Division to the exception list in your firewall. If it doesn't work, check and see if ubisoft is set to offline mode as well.
I didn't find the right solution from the internet.