Most of the MP3 on this site have a sample rate of 22.05Khz. The MPEG-1 Audio Layer III standard supports 32, 44.1 and 48 kHz while the MPEG-2 Audio Layer III extensions add 16, 22.05 and 24 kHz. I suspect your player does not support the 22.05KHz sample rate. See
http://en.wikipedia.org/wiki/MP3#Bit_rateThe best answer is to try a different MP3 player.
You could always convert them from 22.05Khz to 44.1Khz, though the up conversion will degrade the sound quality slightly. One way to do this is to install and use the free Audacity program (Beta) with the Lame MP3 encoder. Open the program, load the MP3 file, set the "Project Rate" in the lower left corner of the program window to 44100, and then select File->Export, set "Save as type" to "MP3 Files", and select the "options" to set your size vs quality settings.