Hi tOnee1 & cholla,
I am glad to inform you, that I solved the problem, however I can blame only myself, why it took me so long. I have 2 sound cards: One of them, Creativ's X-Fi Xtreame Audio, is installed in my PC, and the other one, a portable M-Audio's Fast Track Pro sound card, is connected to my PC with a USB cable and is connected by a cable to my Stereo system. The reason for that is, that I am transmiting music from my LP Records into my PC and this way the quality of the sound that comes to Creativ's card is better, then it would be if it came to the Creativ's card directly from my stereo system. Therefore, usually, the settings in my Control Panel > Sounds and Sound devices are: device for listening "Fast Track Pro out" and the device for recording "X-Fi Xtreame Audio". Now, as you undoubtadly know, unlike sounds that are "comming" into the PC from the stereo system, sounds created within the PC, like by playing an audio file from the hard disk, are passing the sound card installed in the PC, and not the external Fast Track Pro sound card. Hence, before I started to record with Audacity the "problematic" MP3, I was supposed to change the setting of the Control Panel > Sounds and Sound devices, so that "device for listening" should also be the Creativ's card and not the external card. Alas, I forgot about that. True, this way at the time of the recording with Audacity I don't here the played file, however I see that Audacity is recording. Incidentally, the specific short song, very funny, was, probably, recorded privatly, so I had no chance to find it.