Connect the terminal application to the serial port for your board. The baud rate is irrelevant.
Send data by typing. Everything you type should be echoed back. To send data, some terminal applications, like Serial Monitor, require pressing the Enter key or clicking a Send button. If exactly what you send is echoed back then the board passes the test. This means that the host computer hardware driver, USB cable, and USB to serial converter are all working.
Does that work or not? If not, try a different USB cable. Still no go? Then likely the USB/Serial adapter chip got fried, and the '328P may be ok.