If I might make a suggestion:
If you haven't done so recently, to borrow a term from the computer world, reboot. Sometimes the Link seems to have a bit of trouble locking onto the right signal. Occasionally (very occasionally) I've had this problem with mine.
Have you tried hooking the CD player up by its analog outs, to see if maybe the amp is the problem? When you finish with that, run the analog outs through the analog pass-thru in the Link. This may indicate whether the problem is with your DAC.
One other possibility (please don't take this the wrong way) is that you need to spend a bit more time with the Link DAC. When I first hooked mine up, I have to admit that I was disappointed. The bass seemed less powerful, and the treble seemed rolled off. After listening for a few more days, however, I realized that it wasn't that the bass was weak...it was actually nice and tight, and not overpresented. The treble was less harsh, not rolled off. The more I listened to it, the more and more I liked what I was hearing. Maybe it will work that way for you as well.
Hope this helps....