Did you make sure to output the mp3 to .wav format before burning it to an audio CD? If you burn just the mp3s, it won't work in a regular CD player. You need to change the file format to a .wav.
That can be done really simply using WinAmp. Just go to Options, then Preferences. Under Plug-Ins, click on Output and then choose the Disk Writer plugin, called out_disk.dll. Make sure to click the "configure" button to choose what folder you want the files written to. Then, just play the files in winamp like you normally would. This will output the mp3s to a .wav file. Take these files and burn THEM to the CD.
Hope this helps