Windows computers aside, a blue
screen in the video world is the universal indicator of "Hey, I ain't got no stinking video signal!". The Roland
switcher supports the usual two outputs of a
switcher: Program and
Preview. The controls on the Roland let you select which
HDMI input goes to Program and which goes to
Preview. It embeds the incoming analog audio into both of those outputs.
If your "
Preview"
monitor has audio, then the Roland
switcher is properly embedding the analog audio into the
HDMI video from the camera and sending it "downstream". Unless there's a separate setting on the Roland for audio embedding (I doubt it), I'd assume your program
HDMI output is also getting audio. A simple test is to
plug your
PREVIEW monitor into the PROGRAM output of the
switcher and see if you are getting video and audio. If you are not, then you know to look at the Roland settings or possibly
send it in for repair.
If you are in fact getting video and audio in the PROGRAM output from the
switcher, it sounds like it then goes into a USB video interface box that converts the
HDMI signal to look like a USB webcam to the laptop. I am allergic to Windows so I can't guide you on that but on the Macintosh, there is an audio control panel that lets you choose the default audio input. I'd make sure I have the audio input set to use the USB input and then make sure OBS is set to use the USB device for audio.
If your USB video interface is working, you may find that somehow OBS and the Roland
switcher are set to different video modes. Devices like monitors and video interfaces support a range of modes and typically automatically adapt to the incoming signal. Your Roland
switcher supports 1080p, 1080i and 720p
HDMI modes. On a low end
switcher like yours, this is a global setting that will apply to all inputs and outputs. Your camera must be set to output what your Roland is set at. Your video interface has a set of modes it supports. You might have set the Roland to a mode that your interface does not support. Pretty much everything these days will work with 720p so you could start by setting OBS, Sony and Roland to 720p and see if that gets you back.