burninfool has given you good advice.
To reiterate his advice:
Check to see that the MP3 files are CBR (constant bit rate) with ID3v1 tags.
In Nero, go to New Compilation | CD-ROM (ISO)
Multisession = No Multisession
ISO = Level 1, Mode 1, ISO 9660 Character Set, Unselect Joliet, Unselect all Relax ISO Restrictions
Burn = Disk-at-Once, select Finalize CD
You can leave the MP3 files in the root directory, but you can also put them in folders by right clicking on the New button in the left pane of the burn dialog. Click on Create Folder and insert a name up to 8 characters in length. Drag the MP3's to the folder(s) and burn.
If the link posted above doesn't seem to be working, try CDex 1.50
The file downloads are not working, but I have downloaded it at ftp://files.3dnews.ru/pub/cd/cdex_150.exe