Okay. So that little chip is a USB to Serial converter which allows communication with the big chip on the board. Often times with clones (boards not made by Arduino) such as your Elegoo, this chip can be different, and therefore not recognizable by the IDE or the computer. Your chip seems to be okay, so it must be something else.
First, try to connect your board to another computer and see if anything different happens. If that doesn't work, try a different cable. Some cables are solely meant for charging, and do not carry any signals except for power and ground. As such the device will only receive power, but will not show up in any ports or in the IDE.