When you play a BluRay with menus for the first time, MC is downloading java64 and libbluray64 and places them in your "%APPDATA%\J River\Media Center 29\Plugins" folder. Check if you have them. If they're not there maybe something is preventing MC from downloading them.
If you have them you can remove them just for a simple test and let MC download them again.
MC sometimes doesn't work with a BluRay in menus mode if the region of the BluRay is not the same as the Blu-ray Region Code in the MC settings.
Also, check if you don't have JAVA_HOME or JRE_HOME defined as user environment variables. I don't know if the libbluray bundled with MC is modified to ignore them. If you have them, then you likely have "C:\Program Files (x86)\Common Files\Oracle\Java\javapath" or "C:\Program Files\Common Files\Oracle\Java\javapath" added to your PATH system environment variable as well. This means a different Java installation on your system will be used instead of the one that comes with MC, and that version of Java might not be supported.