Are you saying that Premiere Elements 13/13.1 and 14 both cannot recognize your burner in the burn to area of versions? Did you mean 13 could not..... instead of 13 could find.... when you wrote
13 could find a drive to burn to and now I have the same problem Elements 14
I am assuming that both versions did not work in this regard. So...
1. What troubleshooting did you do in 13/13.1 to try to resolve this matter?
If you cannot burn to Type: Disc in 14, can you burn to Type: ISO Image in 14? What is your burner - Blu-ray DVD/CD or DVD/CD?
How many burners do you have (internal and external), and what other burn software do you have on that computer?
Can we assume that you have the latest version of QuickTime installed on your computer and that you are running the programs as administrator (from user account with administrative privileges)? In addition to that, right click the desktop icon of Premiere Elements 14, select and apply Run As Administrator. Did that resolve the issue of burner recognition in 14?
Please consider. Any questions, please do not hesitate to ask.