Mednafen and beetle are the same core, its called beetle in the UI, but its actually mednafen.
Do you have the bios files for PS1? and as always, do the games work in the emulator by themselves? That should ALWAYS be what you do first, get the emulator working with your games then, import to launchbox, that we we can isolate the issue to Launchbox and that makes troubleshooting far easier.