With the Creative Suite, you had two activation slots (two machines). To activate a third installation, you had to deactivate one of the others.
If you didn't, or couldn't, e.g. because of a disk crash, Adobe could until recently reset your activation count if you contacted them.
They no longer do that.
So the only option now is to deactivate on the old machine before you install on the new machine. If you still have access to the old machine, do that ASAP. If not, there isn't anything you can do. Trying to reinstall on the old machine will just count as a new install requiring a new activation.