Okay - I've reinstalled the IDE (Arduino 1.6.8 - 1.6.9 has install errors) on my PC (Windows10, 64-bit) and still get the error when I upload the code to an Arduino UNO. The Board is identified in the IDE as an Arduino/Genuino UNO (which it is), connected to port "COM5(Arduino/Genuino Uno)". I'm using the programmer "AVRISP mkII" to do the updates. Compiles fine, then the LED's flash and the "Port Busy" error shows up.
I am connected to digital pins 0 and 1 in the sketch - is this a problem? If so, is there any way to override the default RX/TX mode to allow the pins to be used as general I/O?
The pins 0 and 1 are used for serial communication and should not be used for any other function. Try modifying the code and change the pins. That should proabably help you. 
You can change the serial pins with the “softserial” libs.
Look it up for specifics and examples.
It seems the hardware won't allow my configuration - I need just one more I/O port. So I'll have to use a different board. Thanks for the suggestions. The clearest explanation was in the schematics - TX and RX are connected to the UART chip via resistors. No chance to reconfigure without cutting traces on the board.