Sorry to hear that you can no longer use Photoshop Elements 13 is not working as it's showing up as Trail.
It's possible that your computer could have trouble connecting to Adobe's activation servers while activating the product. This could be because of an incorrectly configured Operating System hosts file (Operating system hosts files maphost namesto IP addresses).
To solve this issue, try removing Adobe-relatedentriesfrom thehostsfile. You can remove the Adobe-relatedentriesfrom thehostsfile in two ways:
Automatically repair the hosts file using the Limited Access Repair tool: Repair thehostsfile using the Limited Access Repair tool. With this method, you do not have to manually edit thehostsfile -- the tool automatically repairs the file.