Ok, so the question is then how to find a player that sounds like the old Cal Audio, other than trial and error?
TEchnically, impedance matching between source and pre-amp is the only thing I know of that matters, so if those specs look good, that is a first step, but stil not a guarantee. Individual CD players will still sound different from there, this just helps assure that the CD is a good match electronically to your pre-amp.
From there, it is mostly hearsay and trial and error, what you decide to try based on others comments, reviews, recommendations, etc. If you get lucky, you'll find something that sounds like what you had before.
I think the point is regarding the amp is that if you are in a good position to start with regarding the amp optimally driving the speakers, based primarily on amp power, current and efficiency at 8 and 4 ohms, then you will have a better chance of finding a player that sounds good rather than having to find a player that is not handicapped in your system and perhaps can make up for the shortcomings due to amplification.
The other fast track to the happy path would be to find another Cal Audio Icon MkII player used to replace what you had, but the challenge there might be to find one that is in good operating condition and stays that way. I had to fix mine twice at considerable cost before I finally decided to ditch it, so I would be cautious going this way as well if it were me.
Another thought I had is that perhaps if your current CD player finally died that perhaps it was not oeprating up to spec as well beforehand and that was part of the problem? That's just pure speculation on my part however though.
Good luck!