I'd suggest getting a DAC instead of a new CD player... Also for $1K (much less used) I'd suggest the Benchmark DAC1 if you want a neutral and detailed sound... if you are looking for a warmer sound, I've heard that the PS Audio DLink iii and the Van Alstine DACs should be able to provide that...

I'm not sure that the cheaper DACs such as the Music Hall, Cambridge Audio Dacmagic or Musical Fidelity VDAC will offer much, if any, improvement over the sound quality of your existing CD player.