check lsmod (as root) to see if there is a module for your sound card present (Red Hat uses modules for this from memory)
check alsamixer to make sure sound is configured to run
grab mpg123 (unless you have it) and point it at some files to play (it's command line based)
if you still don't hear anything it should at least give you an error message
ls -op /dev/dsp* to see if you have access to the dsp subsystem
chmod 777 /dev/dsp (as root) -- though that isn't the neatest way to do it no one has ever pointed out what would be more appropriate.
check mpg123 again (no point in doing the above two steps if mpg already worked or told you another cause of error)
IF your mp3s still don't play, bitchin' ... let us know
on to audio cd, ensure your player is looking at the right drive /dev/hd* (where * is a for IDE1 Master, b for IDE1 Slave, c for IDE2 Master, and d for IDE2 Slave). You CAN go with /dev/cdrom, in which case you want to check it's symlinked to /dev/hd*.
NOW, there is a lie in the above statement. (potentially) if your burner is configured for some reason as a SCSI, with no IDE-CDROM support (highly unlikely unless you compiled your own kernel). it will be linked to /dev/sg or /dev/sd (both followed by a number (0 or 1, using similar logic to the hd* thing). IF this is the case , cat /etc/fstab and it will tell you what your cdrom mount point actually points at..
IF CD player and alsa are configured right, and the cd player works in windows you should get sound. BUT don't be fooled by windows giving you audio cd access, some players in windows can be configured to use your IDE cable to transfer audio data (better quality sound), i doubt this can be done in linux, without trying).
lastly if alsamixer was misconfigured, ie mutes and so forth, as root run
Let us know how you go.