DAC or CD Player. Help!

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!  

Thanks to everyone for helping me out!

I get the point of what people are saying with "synergy," but unless you live in an audio shop, who has the money to throw a grand or two here and there to determine which component of the many they read about is 'the one' to mate with components they already own? I have to conclude that a lot of what 'synergy' means is whatever the poster thinks sounds good at that moment. Until he buys something else, of course, at which point the synergy changes to that. 
PS: expensive cables do. not. matter.