I have a Raspberry Pi 3 Model B, and I'm trying to use my laptop screen as display for the Pi. I had followed various tutorials for this none of it is working. I found that laptop couldn't detect the Pi when connected to the Ethernet port and even not blinking on either side port when connected. When I connected them using a router, even the router couldn't detect the Pi. What can be solution for this?
Modern ethernet devices usually support Auto-Mdi-X.
If for whatever reason this doesn't work or isn't supported you'll need a crossover cable directly connecting the two.
Or use a device like a hub/switch/router to connect them with normal straight through patch cables.
For the router not detecting the pi - check with a different cable, the one you used might be broken.