How connect the Arduino UNO with serial cable to computer?

Hello all,
I have an new Arduino UNO and he works on USB fine. The ASCII-example sketch also works fine on USB with serial monitor tool.
Now I want the Arduino UNO connected with serial cable to the computer. This serial cable works fine with other devices.
The Arduino UNO has TX,RX and GND (pins) only. I disconnected USB cable and connected TX, RX and GND to the serial cable (TX-RX, RX-TX, GND-GND). I tested with the serial monitor tool, the baud rate and the serial port was right.
Now the ASCII-example sketch do not work.

Question: How is the Arduino UNO connected with/to serial cable to computer that the ASCII-example sketch works fine ?

Thanks for answers.

be aware that the voltage levels of Arduino serial are TTL (0..5V) while a standard serial port of a PC are up to 12V.

You need a level convertor to solve this voltage difference, not using one will damage your duino.

Not only is the voltage too high it also goes to negative 12V.
Plus the fact that the signal level is inverted means you need a converter.
Something like a MAX202 chip or similar.

Thanks, I will use MAX202 …