Bit bang ATmega328 with Arduino bootloader using AVRDUDE
How about making one of the countless serial AVR programmers and using it to write the Arduino firmware? This one worked for me, but I have USB to serial converter, so it works at amazing 3 B/s. If the programer lines on your other project are available, you can dump firmware using AVRdude. You could also probably get it form the Internet, but I don't know where to look