You should definately get a proper transport. I have recently compared my Theta Data Basic II to Marantz CD 63 KI Signature - which is a great CD player - and the difference was not subtle. More air, better resolution and much smoother sound.
Digital cable, although important, doesn't make such a dramatic difference as transport itself.
You can get a Theta Data Basic II in mint condition for as little as 500$ used.
I have also recently found and bought a Muse Model 5 CDT for a friend for a mere 350$. It is also a very good transport.