Make sure you don't have multiple copies of sql dev or Java JDK installed.
It could be finding an older version of Java.
Try opening a command line console and run <sqldev_home>\sqldeveloper\sqldeveloper\bin\sqldeveloper.exe from there. Possibly some messages will appear in the console during this delay/hang, or you can obtain a full thread dump of what's happening in the JVM via the jstack utility or a Ctrl-Break (but make sure the console screen buffer size property is large so as not to truncate the output).
Such hangs may occur when SQL Developer cannot write to the user settings folder (typically C:\Users\<your-userid>\AppData\Roaming) either due to privilege issues or placement on a network drive, etc.