Well, it turns out that the problem was on my end. I found a complaint/problem form to contact hotmail, and they got back to me quickly with a few suggestions. They said that I should lower my security settings to the default ones, which didn't work, gave me 7 MSN sites to try to sign into with my .NET passport, which didn't work, and finally to try to log in from another computer, which did work. I replied to them to let them know that I was only having trouble from my home computer and they e-mailed back a few hours later with some more suggestions that didn't help. But I got to thinking that maybe I'd blocked the wrong cookie when my security settings were higher (I was accepting first-party cookies and being prompted for third-party cookies, which I blocked), so here's what I did that finally fixed the problem:

went to Internet Options
clicked on the Privacy tab
under Web Sites, I clicked Edit
on that page I clicked Remove All to clear all blocked cookies

After doing that I was able to access my hotmail account.