You have to install Adobe Programs from the original installers. Never migrate from any backup.
Normally Adobe activation should recognize a computer when the hardware was not changed.
If not, you have to contact Adobe's support.
Thank you both for your help. Adobe support chat had me using a License Recovery app from their website; however, it wouldn't launch in Yosemite. Don't know if it could have worked. The fix was to reinstall the applications. I think you're right, Willi. That's the only way for my situation.