Does my Nano have a bad pin?

I've experimented with the Uno V3 and decided to make a game show buzzer system with 6 buttons for a Jeopardy style game we play at my volunteer fire station. Wanting to keep my V3 to prototype and play with I ordered an off-brand Nano V3 with the Atmel MEGA328P to put in a project box to run the system. The program didn't work, station 1 would always buzz in immediately. The buttons on the six pins have the internal software driven pull-up resistors and are pulled LOW when pressed. Using a different sketch using Serial as diagnostics I found pin 13 is always pulled LOW and the LED on the board is dimly lit when the pull-up resistor is on. I believe I have a bad pin but being this is the first Nano I've touched I figured I would ask if it is different from the Uno in this way.

I have extra pins on the board so I just moved that button from pin 13 to pin 7 and it worked fine. I'm asking for reference to this board type.

All the information is available online.

If you check the schematics, you see that both have the system led at pin 13.
The Arduino Nano has a resistor and a led, but the Arduino Uno has an extra gate, to avoid any influence of the led.

Therefor the Arduino Uno can use pin 13 as input, but for the Arduino Nano you better use pin 13 only as output.

Pin 0 and 1 are often used for the serial communication to the computer. So stay away from pin 0,1,13 if you can.

Thank you for the information. Thats just the answer I was looking for.

Therefor the Arduino Uno can use pin 13 as input, but for the Arduino Nano you better use pin 13 only as output.

Baloney. Just add an external 10K pullup resistor if the internal 20K to 50K pullup is not providing a good enough high with your external switch.

CrossRoads:
Baloney.

Spoken too soon. The Arduino Nan0 3.0 has a 680 ohm resistor with led to ground at pin 13.

That's a 4-5mA, so maybe a weak output from elsewhere might have a little trouble driving it.

Caltoa:
Spoken too soon. The Arduino Nan0 3.0 has a 680 ohm resistor with led to ground at pin 13.

The trick here is - it also depends on the colour of the LED which acts as a "clamp" on weak inputs.

A red LED will tend to pull the input "low", but a green or blue probably will not.