Have had the same problem for months on a Windows 10 Pro. PC; suspect it coincided with a Windows update or registry edit. Have tried to find a workaround on Adobe forum but all the answers don't give the 'how to'. Tried reinstalling Photoshop 14 to no avail. The welcome icon is on the taskbar and shows the welcome screen but won't open or close.
@desmondh36796584, I don't know if this will work for you, but some Windows users with similar problems have fixed it by installing the free Creative Cloud desktop application. There is no need to subscribe to anything. Just install the application and see what happens. Please report back if it works for you.