Perform a "loop-back test"...
• Disconnect power from the board
• Remove all connections and shields from the board
• Force the processor to remain in reset by connecting a jumper from RESET to GND
• Connect a jumper from pin 0 to pin 1
• Connect the board to your computer
• Start your favourite terminal application (Serial Monitor will work)
• 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.
• Shutdown the terminal application
• Disconnect the board from the computer
• Remove the two jumpers
Does that work?