What computer operating system? Have you installed the 13.1 Update yet using an opened project's Help Menu/Updates.
To your immediate question....
1. Are you working with an Internet connection?
2. Do you have the latest version of QuickTime installed on your computer - QuickTime 7.7.6 if Windows 10, and QuickTime 7.7.8 if Windows 7, 8, or 8.1 64 bit?
3. Are you running the programs as administrator (from user account with administrative privileges). In addition, have you right clicked the Premiere Elements desktop icon and selected and applied Run As Administrator?
4. What is the save location that you have selected for your Publish+Share/Computer/MPEG export? What MPEG preset is being selected?
Did you check the permissions for the folder that is to receive this export?
Let us start here and then decide what next based on the details in your reply. Depending on your further details, the following Adobe document on Premiere Elements Compiling Errors might me looked at.
1. Internet yes
2. QuickTime 7.7.7
3.Run Premiere Elements as administrator the problem is solved. Thank you very much.
Great news. Great follow through to gain your success.
If everything is working for Premiere Elements 13 on Windows 10, then best do not change anything.
But, things to change if you have to....
a. QuickTime 7.7.6 instead of 7.7.7 QuickTime 7.7.6 for Windows
b. Update 13 to 13.1 using an opened project's Help Menu/Updates. The features of the free 13.1 Update are found
But, right now, looking good and no changes necessary in your present working setup.