Please clarify what version of Premiere Elements is involved? We may be losing something in the translation.
What I seem to be getting from the translation is that
a. You had Premiere Elements 12/12.1 for a few months, and decided to try the current version 13/13.1
b. After 30 days, your 13 tryout expired.
c. You decided to buy 13 and cannot get it to work.
Is that the situation? If not, please correct the above, giving the details again for what has happened to you.
Assuming I understood your issue....
1. Does Premiere Elements 12/12.1 still work on the same computer?
2. When you say that Premiere Elements 13 does not work, what is not working...
a. you cannot open a new project
b. one or more of the features does not work
c. you import source media and the program freezes or crashes
Do you get any error messages associated with 13 not working?
Does the problem exist with or without the antivirus and firewall(s) disabled?
Do you have the latest version of QuickTime installed on the computer with Premiere Elements 13?
Are you running the programs as administrator?
Is your video card/graphics card up to date according to the web site of the manufacturer of the card or the computer?
Others, for later, if necessary.
Please review and consider. The end may be
b. free ccleaner run through (regular and registry part) - (to get rid of leftovers from incomplete uninstalls reinstalls)
c. reinstall with antivirus and firewall(s) disabled
d. then, download and install of 13.1 Update from an opened project's Help Menu/Updates.
Please review and consider, and supply more information. If you need clarification on any of the above, please ask.