In DOS mode, run MEM /C to see if MSCDEX is displayed in the list of drivers. If it is not, your MSCDEX.EXE file may be corrupt, missing, or improperly syntaxed in either the CONFIG.SYS or the AUTOEXEC.BAT file. Be sure the /D switch is identical for the low-level driver and MSCDEX.
If MSCDEX is listed in MEM, look to your hardware. Has the location of the connection been changed--that is, was it connected to an IDE connector and now to the sound card or vice versa? Be sure the ribbon (signal) cable is securely fastened and not reversed on the connector and the Molex (power) connector is also securely fastened (does the power light come on during POST?). Also, the ribbon cable itself may be bad; try it with another cable.
Go into CMOS and run "Auto Detect" for HDDs and see if it will detect it there.
Enter "device=[path]\setver.exe" into CONFIG.SYS. Although DOS should not require it if you have later than DOS 5.0, it has been known to make a difference for some reason.
If you have a "lastdrive=[x]" command in CONFIG.SYS, be sure the specified letter is beyond that which the CD-ROM is supposed to occupy.
There is an outside chance the drive controller itself may have gone bad. If you have it plugged into a connector on the motherboard, change it to the sound card if it has an accomodation for it (or vice versa). If you hook it to the sound card, run a hardware search in Windows (Control Panel > Add New Hardware) and see if Windows will install it through the sound card drivers. (It is best in this case to allow Windows do all the searching and not specify that you want to find your own driver.) You may have to go to either the sound card or CD-ROM manufacturer's web site to see if they have a real mode driver to enable it in DOS. It may be that you will have to get one there to get it to operate even in Windows. Of course, the alternative to this would be to replace the controller outright.