You are probably good to go on the new computer with Premiere Elements, but the moment of truth for Premiere Elements will come when you opt to install it also on another of your computers. If Premiere Elements was never deactivated from the first computer, it will still constitute an install. (Premiere Elements s/n on only 2 of your computers allowed)
So, best pass all this by the Adobe Chat line which should be able to make sure your account is as it should be with just that one install of Premiere Elements with its purchased serial number on the new computer.
The link for the Adobe Chat line is
Please let us know the outcome.
Add On Note: Just in case note, you do not Activate Premiere Elements via Help Menu. But you do Deactivate there. When you enter your serial number in the pop up, I believe that will get the Activation in full gear.
This is a user to user forum, not Adobe support... you will need to talk to Adobe
There is also a Forum for Download & Install & Setup issues
Thank you for the link ATR. I have just discussed with Adobe and he has deactivated 1 machine for Premiere. I do not need to activate either product on the new machine. It is showing them already. I had assumed I needed to activate a second time. All is well and thank you for explanation.
Thanks for the follow up. That Adobe Chat is great for this type of Premiere Elements activation issues. It helped me not so long ago and did it quickly and professionally.