You should have two "live" installations available for Premiere Elements 13.
Is the program installed on another computer? If not, you should have no problem installing it and logging in with your Adobe ID to activate it on your new hard drive.
In fact, it is actually installed on my laptop and my desktop but it doesn't work on the desktop now.
You'll need to contact Adobe customer service and ask them to release one of your activated installs.
What computer operating system is involved with your Premiere Elements 13 issue?
Are you getting a message about you already having the purchased activated serial number on two of your computers when you do not?
If not, I do not believe that Adobe Chat activation is going to help you. But, you could ask nonetheless.
Adobe ID, Signing In
Adobe ID, Sign In, Account Help
If the link does not hold its set, you will need to navigate to the Chat Panel using the above titles as guides.
If you get no help from Chat Panel, then, if you have not done so already, do
b. free ccleaner run through to get rid of leftovers from incomplete uninstalls/reinstalls
c. reinstall with antivirus and firewall(s) disabled
d. download and install of 13.1 Update using an opened project's Help Menu/Updates
Please tell us what is the exact error message while activating it
As I said, I had PE13 installed on my desktop & laptop but I format my Hard Drive Disk (and Windows), so when I installed again PE13 on my desktop, it said that my limit to use has been reached (or something like that, I don't have my desktop near me actually).
When using Adobe "automatic help" it said to contact customer support accross chat or forum, but the problem is that my "old" desktop is still considered as "functionnal" so I can't activate it again on my "new" desktop.
Steve understood it: "ask them to release one of your activated installs"
In fact I just don't get time to chat with adobe customer service (I'm Greenwich +1UTC).