Console connections in puTTY are slightly more complicated. After clicking on the serial option, you are asked for a “Serial line” with the default value “COM1”. COM1 on a Windows machine corresponds to a specific port on your machine. When using the serial-to-usb converter, you should connect the serial cable (the light blue one) to the converter, the serial plug into the router/switch, then usb port into your laptop/computer.
To figure out which COM port you are using, open Device Manager. On Windows 10, you can do this by clicking the Windows button and searching for “Device Manager”. The process should be similar if not identical on other Windows machines. Something like this should pop up: