OBS Studio has historically been known to 'lock' sources to avoid conflicts, delays, etc. Which makes me wonder if you have something else attached/connected to the video source, and that is preventing OBS Studio from accessing it? But, if you are hearing the audio, a settings issue does seem probable
1. don't ignore the pinned post in this forum about posting OBS Studio log when asking for help
2. clean OS reboot, stopping anything in the background not needed (for testing purposes)
3. try a new Scene collection, with NO filters/effects/plugins, etc
and try adding your capture card video as a source again
Look into driver settings if you are dealing with interlaced video source, or whether the Elgato expects your capture source to re-interlace the video for you (and what you have to do in OBS Studio to make that happen)