I am sure a lot of your face this particular Hotmail sign in problem - the page refuses to load on your computer... it simply cannot be opened in a browser window. I empathize, because I too faced this troubling issue sometime back. You know you aren't doing anything wrong because you are actually not doing anything!
This is what I went through.
I was trying to access Hotmail sign in page from Firefox browser. The browser window kept showing me it was busy but nothing happened even after a couple of minutes. No download... absolutely nothing!
I tried different Hotmail sign in page URLs I knew - www.hotmail.com, mail.live.com and home.live.com - and none of these loaded.
I then shifted to Internet Explorer thinking maybe, just maybe, this would work as it's a Microsoft product just like Hotmail... but in vain. I just couldn't get Hotmail to open.
Assuming something was wrong with my computer I checked from another system that was using the same internet connection (through WLAN). Hotmail sign in page opened without any problem. And so I concluded there was indeed a problem with my computer. The net connection was fine, other web sites were giving no trouble then why was Hotmail refusing to load?
Still working from Internet Explorer, I started to check the browser connection settings. And was quickly able to come up with a solution which might work for you.
Start Internet Explorer and go to Tools -> Internet Options.

Now go to the "Advanced" tab and move down to the HTTP 1.1 settings section. Uncheck Use HTTP 1.1 and check Use HTTP 1.1 through proxy connections. Now click on the Apply button and then the OK button.

Close the browser window and then restart the program. Type www.hotmail.com and yippee! It works!
Note: This solution might not work for you because the same problem of "Hotmail page does not open" can be because of a different reason not connected to HTTP 1.1 settings. I suggest you first troubleshoot your problem; refer the steps above on how I concluded that it must be the net settings of my system which are causing such headaches. But yes, I would definitely like to know more about your specific issue. Send me a mail and I do promise spending a little time on it.
Page contents: Cannot open Hotmail sign in page? Here is a solution to one of the most common problems "plaguing" the Hotmail email service.
Comments, questions, feedback... whatever!