One of my Azure free trial accounts got cancelled by mistake and want to uncancel it so I don't lose all of my resources.  How would I go about doing that? 

Hi,

Sorry to hear that. You can try to call the customer service to open a support ticket for you, but I am not sure they can re-new the account:

http://support.microsoft.com/gp/customer-service-phone-numbers?wa=wsignin1.0

Or can you send email to azure portal or account team to get help directly? From my side I have no right to take any action on the account.

Thanks,