Sometimes a reinstall onto another computer can make Microsoft think you are installing the same license onto two computers, thereby violating the license terms. Did you uninstall the software from the old computer before trying to install it onto the new computer? This will let Microsoft know that you have removed it from the old computer, which should free up the license for the new computer. Be sure to do a backup of your old computer before uninstalling Office; that way, you can at least have one way of accessing Office, if you can't get Office activated on the new computer.
That is a very good possible explanation as to what may have happened.

Mary. I will be very interested in hearing back from you if & when you get this problem sorted out.