You do this: search Google using a phrase like "photoshop essentials 12 ID number is invalid". You won't find a valid number, but you will find a long list of forum posts on that topic, and possibly find the answer to why yours doesn't work, because you can bet that no matter what the problem is, you are not the only one to have it. Search for exactly what you want. Use the exact error message. Be specific.
I find the answers to virtually every computer hardware or software issue this way. I honestly don't remember the last time I called CS for any of this stuff. It's often, as you have found, a waste of time playing phone tag with poorly trained workers who know little more than what they read on the script in front of them.