retro: All baud rates above 9600 produce the same " junk " values.
OK, Which PC OS are you using and what version of the Arduino IDE software?
Edit PS:
The Arduino bootloader for your NANO uploads new sketches at 57600 baud, so the fact that you can upload new programs says it's not just the speeds that you are trying to use, but rather some software problem.
Are you running that actual sample code? In your other post, you say you are taking analog readings. Have you tried temproarily disconnecting the analog circuitry and just running the sample code with no other connections?
I don't think it has anything to do with the mini-USB connection. If you are setting 9600 baud in the code, the Arduino is actually using 9615.38 baud which is close enough (i.e., UBRR0 register = 103). At 14400, the UBRR0 register is 68 which gives an actual baud rate of 14492.75. That is also plenty close.
Have you tried it with HyperTerminal or some other terminal program instead of the serial monitor? Also, try 19200 instead of 14400 just for kicks. 19200 is a more commonly used baud rate anyway. Post the actual junk that comes out at 19200 in case someone wants to take the time and analyze it down to the bit level to determine what's really going on.
The problem was somehow fixed last night. I removed a resistor I had connected to one of the digital pins and to TX pin (I thought it was connected to ground, but I accidentally had it connected to TX). I still don't understand how this fixed the problem / why it caused the problem in the first place but thank you all for answering my questions! I am now communicating at 115200 baud rate!!!! ;D