Hotmail is owned my Microsoft, so you'll have to get into contact with them to get it sorted out. I really hope it's not connected to an xbox account, because then it gets into credit card messes, and those are hell to sort out.
The good thing about it getting shut down, is if you fail to put in the right password, or security question enough times (3 I think), then it's locked down for everyone. Including the hackers. Keep doing that. At the very least it'll annoy the heck out of them and they'll eventually give it up.
However, hacking is less likely, and it's more likely you got caught by a keylogger, or phisher of some kind (Run all virus scans now!). Though there are situations where there have been hard hacks to get past simple passwords. It's likely they were hoping that your hotmail is attached to an xbox live account, so that they could wrack up charges, and shift the points/games to another account. Also known as the FIFA scam.
Happened to me about a year ago (while I was online at the time!), so now I go about changing my password every month. Fortunately I got it sorted, unfortunately I didn't get my money back, but I did get to keep the points, and they let me pick a new game.
So far all I can suggest is that you go through Hotmail's silly web forms for hacked accounts. I don't know how long it takes for them to get back to you, because I jumped on Xbox support numbers, and that seemed to speed things up.
Good luck!