If you logon/look in your my.avast.com account under the license section of your account I believe it should say that you have assigned the license to a device (your old PC) and if you have another you can assign.
Though unless you specifically purchased a multi PC license at the time, then in all likelihood it is for a single PC.
Do you still have the email that was sent to you upon purchase (and attached license file) ?
That should say what you purchased.
