Very often such behavior is the result of a video driver not playing well with Java. Try this...
1. Open a Cmd console from the ...\sqldeveloper\sqldeveloper\bin directory
2. Launch sqldeveloper.exe
3. If the JVM crashes, you will see a dump with some clues. Perhaps about a driver, or some issue with your environment.
If there is no dump, try renaming or deleting the SQL Developer settings for 4.1.5 under C:\Users\<youruser>\AppData\Roaming and restart SQL Developer.