Try opening a CMD console window and running the sqldeveloper.exe in the sqldeveloper\sqldeveloper\bin folder directly from there. Perhaps some useful error messages will display in the console. This behavior may be due to lack of write access to the user profile folder -- possibly some administrative rules in the way, or it is located on a network drive, etc.
If that is the case, and write privileges cannot be easily obtained, you can always force the user settings into an alternate location by adding the following to the sqldeveloper.conf file in the bin directory....
Thanks for the help. As you said, I ran by cmd console in sqldeveloper\sqldeveloper\bin and it opened.