Remote Desktop relies on Windows XP passwords for login. If you don't currently have a password configured for your account, or if your password is something simple, change it. At minimum, your password should be 10-12 characters long, with a combination of numbers, letters and special characters. This password is no longer just designed to keep out your roommate or family members, it's going to keep the entire Internet from accessing your computer.
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Try using various remote support tools such as gosupportnow, logmeinrescue, GoToMyPC etc. in order to establish remote web connection between computers.