Definitely worth contacting Adobe Customer Service about this one, David!
You are allowed two installations on the same Adobe ID. If you've used a different ID or used both of your installations already, you'll need to log off from an installation in order to activate the program on a different computer.
If you bought the program used or from a retailer who may have sold you a previously opened box, you should contact that retailer and arrange a refund.
What is the computer operating system for original computer, what is the computer operating system for computer 2.
Are your installs from purchased downloaded installation files or from purchased installation disc?
Also, have you visited your account at Adobe web site, to confirm your product and its serial number? That information should be in your account there once you sign in with your Adobe ID and password.
If problems with your Adobe ID and password, please consider online Adobe Chat group dealing with Adobe ID/Sign In/Account Information, using the following link
Please consider the above.
Add On..."Same purchased activated serial number" instead of Adobe ID.....you are allowed the same purchased activated serial number on no more than 2 of your computers (and those 2 not running at the same time).