Hi Ash,
Sounds like a pretty tough situation
I have found that Hotmail support, while a little slow, are generally fairly helpful. You may get an auto response template back the first couple of times but if you keep responding it should eventually get answered by a human.
At the end of the day, it may be easier for your cousin to simply create a new account and notify her friends of her new address. This is no longer as arduous a task as it used to be, thanks to Facebook, MySpace etc. The most important part of any free email account is the security and this always starts with the password.
Your cousin can generate a random password for anything at
http://www.pctools.com/guides/password/I realise neither suggestion is probably what you're after, but start by giving Hotmail support a chance and let us now how you go.
Good Luck!