Starting Up Photoshop Elements 2021 - Hung Up on PlayerMediaCore.prm

The start-up of which program are you referring to?  Can you get to the Home Screen?  Do you have Premiere Elements installed? Or is this happening when you open the Organizer?

Here is a link to the problem related to Premiere Elements.  The solution requires you to edit a text file (in Notepad).  If you don't have Premiere, I can only find the text file for the Organizer on my machine.  You can try making the same modification to the file at this location:  C:\Users\[YOUR USER NAME]\AppData\Roaming\Adobe\Elements Organizer\19.0.

If you are not comfortable making these changes, I suggest you start a chat with Adobe Support by clicking on the blue Contact Us button under the Support menu on the Adobe.com website.