Same machine.
If boot with Windows 7, outlook.com loads, any browser, I use Firefox most of the time.
If boot with Linux (Ubuntu 14.04 64 bits), outlook.com does not load, blank page, no error messages, all browsers including Google Chrome and Chromium. If boot a guest OS under Virtual Box (Windows XP SP3) the guest OS even being Windows does not load outlook.com, all browsers including IE 8.
In both platforms I'm able to see the login page. It renders fine. But once I input the username and password, in Linux I end with a blank page.
I have also a PC with Windows 8, It loads outlook.com without any problem. I have another Linux PC (Lubuntu 14.10) that I have not tried yet, but I suspects it behavior will be the same than my main PC with Ubuntu.
It is confirmed then that something in Linux is preventing the connection to outlook.com or any of its resources, scripts, etc. I had no messed up with any config file like the host file or something. In case this is relevant, both Linux and Windows 7 have a static IP set for the LAN, but not the same, Windows 7 ends with 3, and Linux ends with 4, even if it is the same machine. Both Linux and Windows have the DNS servers addresses manually set, and both use the same DNS servers.
Using the Network monitoring in Firefox Developer Tools I can only see two urls trying to load, they are:
https://col125.mail.live.com/default.aspx
First one returns code 302. Second one never returns. The loading of the outlook.com web client stops there under Linux.
If I copy and paste second url into browser's address bar, I end with a page that says "Failed secure connection" and asks me to send a report of the problem to Mozilla, I did it.
Don't ask me to clean history, I cannot do that. But I created another profile using Firefox Profile Manager that has a clean history and no addons, and behavior of outlook.com is the same there. I think the problem is in the OS not in the browser. I don't know which component may be causing this. My Ubuntu 14.04 has all updates to date.
Update:
I confirm that Lubuntu 14.10 does the same. Other thing I may try is with a different router, but I cannot do it right now.
Configure the account in Mozilla Thunderbird works. Both as IMAP or POP3, so that is what I'm doing while the web client get fixed. Just add your credentials and select IMAP and let Thunderbird auto configure everything.
Before somebody suggests it, I already tried with the MTU in the router config page. All values I tried (1500, 1492, random number, back to default) worked under Windows and none under Linux.
The problem is that many people occasionally ask me to use outlook.com in this computer for different reasons and configure Thunderbird each time is not practical. For an occasional read of e-mail a private window with the web client is the most practical. I open to any suggestions. Restarting the computer to boot Windows 7 is not something I can do at any time either.