Assuming the device is digital, take two LED's, any two colours. Hook one up to TX and ground and hook the other one to RX and ground. Start your device and make it send data to the port. If one light isn't flashing on and off randomly, then try switching GND with +ve (in other words, connect the LED's to +ve) and try again. Either way, when you make your device send data to the port, one led should blink. If it doesn't, your LED is dead and u must use another LED.
The LED that goes on and off randomly is the result of the TX line.