When I choose "video capture device" and click on gv-usb2, the box shows a blue screen. How can I fix this?

I’ve only seen that when the console is powered off (no video signal = blue screen). Are you picking up the audio from the console or is that not working either?

you need to set the correct settings in the properties of the source in OBS or the gv-usb2 won't be able to understand the signal. For example mine is set to PAL60, so it doesn't pick up the Gamecube booting (which is in PAL50), but will work fine once I've selected 60hz mode during the game boot up process.

Did you swap the video output in the settings on the ps3

Like @whybother88 says, if you were using HDMI with it, you'll need to reset the video mode before you can use SD cables.

Here's the official article: https://support.playstation.com/s/article/Change-PS3-Video-Settings?language=en_US

The gist of which is:

Reset Video Output If you are changing cables or cannot see an image on the screen, you may need to reset the video output to default settings. To reset the video output:

1. While the PS3 system is in standby mode (red light on the front of the system), hold down the touch-sensitive On/Off button on the front of the system until the PS3 beeps a second time (approximately 5 seconds), then release it.
2. The PS3 will power up, the Video Output Settings will automatically reset to the standard resolution (or detect the current display output settings of your TV/monitor).