You can install up to two computers. You can go back to the old one and, under Help, select Deactivate if you want to still use both. If you don't have the old one, you have to comunicate with Adobe to get the "use" back.
Adobe allows you to use the purchased serial number on no more than 2 of your computers but not use the two at the same time.
If you ever get into a situation where you cannot install that purchased serial number on a 3rd computer AND cannot deactivate one of the copies of either of the other 2 computers, Adobe can assist you in that matter even if this purchase serial number is not from the current version of Premiere Elements.
In such a case, you can click on the following link and, when it opens, click on the statement "Still Need Help. Contact us." to bring up the Adobe Chat for the corrective action involving topic "Serial number issues or activating my product."
Any questions or need clarification, please do not hesitate to ask.
It's been awhile since I tried to help anyone.
Apparantly, no matter how simple the answer is, there is no point in trying to help out. A.T. Romano will always take care of you! His thoroughness ensures Adobe's products are well supported.
I am working on getting a moderator to move your Photoshop Elements thread to the Adobe Photoshop Elements Forum to assure that you are fully supported by a Photoshop Elements group.
However, do you have all the information that you need at this point?