In such cases, you could try the following:
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you could try using In-Private Browsing with IE9/10 and see if you are able to enter your credentials then try to use the URL redirecting to domain ID https://manage.windowsazure.com/?whr=microsoft.com
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If you have other live account already included as co-admin or service administrator with your Azure Subscription please use that live account instead.
If none of these seem to work for you, it is possible that your problem is related with lingering ordid issue, where you will have to contact Microsoft Support directly regarding the issue.