When you say you get music thru the earphones, not speakers:
a) can you still, reliably, listen to music? - indicates that the CD transport and DAC are operational, and also power is not an issue.
b) do you start the CD playing with a play button on the drive itself or by using software, e.g. Accessories, CD Player?.
I would suspect the IDE cable, either where it connects to the CD drive, or on the mobo (unless both hdd and cd are on the primary, in which case just at the CD drive). Or, of course, it could be the secondary IDE controller has packed in.
I'm not saying it is impossible, but I have never come across a CD player that could play music CDs but not data CDs.
Of course, it could be a software driver problem - have you installed any hardware or software co-incident with the problem starting? Although driver problems are rarely intermittent or gradually get worse - they tend to be works / doesn't work problems.
Having said all that, a P II 233 and Win 95? I still have an old Tosh laptop that's a similar spec. and despite the limitations of memory (160 MB), graphics, hdd etc. it can still run Win2K (has done for about 4 years now), but with recent apps like Office 2K it was really running like a dog. If you can afford to, think of upgrading to a newer PC (don't even think of trying to upgrade the existing) and OS. Have a look at the Dell outlet site.
SD