DAC or CD Player. Help!

All matters including cable.  Synergy is important.  In case of digital connection it will be output impedance of CDP, input impedance of the DAC and characteristic impedance of the cable.  It will also be length of the cable, slew rate of the CDP etc.  It is a system thing.

RSA,

it all matters!

This isn't very complicated. CD players are just three components built into one box, the transport that picks up the bits from the disc, the built-in DAC (digital to analog converter) and the analog output stage that sends a signal to the preamp or integrated amp. 

They're all important, as others have mentioned, so the question about using a separate DAC really comes down, sonically, to whether the DAC and the analog output stage in your CD player are better than an external DAC and its analog output stage. 

But, one of the big advantages of using an external DAC and relying only on the player for sending the bits to the DAC is that the transport in a CD player will always eventually fail.

They are mechanical devices, like the tires on your car, and they have a limited lifespan. Replacing the transport in a quality CD player can cost more than what you paid for it originally.

DACs are being improved upon daily. Good ones are not that expensive and you're much better set up for the future of music reproduction if you make the move now.

I think some of these responses are more complicated for the OP than they need to be.  In general, the DAC will determine the sound.

I agree that if a disc players transport and digital output is functioning as it should, the DAC used would likely make the greatest contribution to the sonics provided.

I believe that the concept of synergy in the development of a audio system is important. Optimizing electrical (objective) and personal preference (subjective) synergies provides for the greatest enjoyment of any system.

Do I, or will I, ever understand all that this implies? Never. Do enjoy the journey however. Thanks to all those on this forum that have helped me on the way!