Take these steps:
- Power off the board completely
- Remove the USB cable
- Hold down the Reset button
- keep it held down (or, run a jumper wire from the RESET pin to the GND pin).
- Still holding down Reset reconnect the USB cable.
- Start uploading a sketch that does not have this problem (I use the Blink sketch).
- When you see the Receive light blink, release the Reset button
- Change your code and add a delay(3000), or more in setup(). This allows easy recovery from a serial flood.
Note: I have seen this happen several times when I flood the serial output. An indication is the TX light is stuck on.