Open Premiere Elements, go to File and select the Open option.
You can also select Open from Premiere Elements' Welcome Screen.
Unless the Project file (.PREL) has become corrupted, there should be no reason for a Project, created in the trial, to not Open in the full-paid version. The ONLY difference between the two programs is that trial will embed a watermark on the Exported footage.
This FAQ Entry will instruct you on changing the Project, to remove that watermark.