One reason your CD won't play is that it is too scratched. Check the back of the CD. You can clean a CD with a damp cloth. Wipe side-to side, not in a circle. This should remove excess dust and buildup.
Some stereo systems will not play burned CDs. A burned CD is a blank CD that a program such as iTunes or Windows Media Player records with music. It is not the original CD. If your stereo will not play the CD, try it on a different player. You may have to change your car stereo or only use originally-purchased CDs.
An MP3 CD is burned with data files -- the actual MP3s instead of being burned as a music CD. Some stereos will not play this type of file. Use a music program such as iTunes or Windows Media Player to reburn the CD as a music CD. View the Burn settings on the program to determine if the program is burning as an MP3 data CD. Change the settings to burn a music CD, then try to play the new CD.