One major difference between cd players and computers is computers are usually a box of electrical noise and vibration. To bridge the difference, assuming jitter is audible (ha ha ha let's humor Gregorio), you'd be looking at shielding, damping, tweaking, replacing, and removing hardware and software until the computer is like a 10w cd player with a hard drive instead of cd changer. I hope you don't actually want to bridge the difference this way
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Here's some less extreme things to try. Try out cplay software if you are using windows. Many people say it is the best sounding media player. Read the manual or you will have trouble, it has a GUI meant for remote control, and only reads single lossless flac and wav files or playlists so you may need the very quick cuesheet creator also on their site. Generally speaking I think most cd players will be superior to most computers digital output if we don't do any serious tweaks, but a computer does have faster processing and more ram, which this software utilizes well. You'll need asio4all or the not free "usb-audio" software. http://www.cicsmemoryplayer.com/
Since it's cheap, you may want to try a bunch of 14awg power cables from monoprice. Ten would be like $25 shipped, and you won't have to worry about audiophile cables again, but imo I think the improvement is minor for most equipment. Monoprice sells fantastic bang for buck audio cables as well. http://www.monoprice.com/products/search.asp?keyword=14awg+power&x=0&y=0
You could also try a line conditioner for both cd player and computer, but most cheap conditioners will increase noise at certain frequencies. A few people say no line conditioner however expensive is better than straight from the wall, that the cons outweigh the pros. A good conditioner I like for cd players, lcd's and computers, but not speaker amps, is the furman ac-215, but only if you can find it for ~$75 shipped on ebay, not the $200 retail price. The circuitry is the same as their $300 retail conditioner, just less sockets so you may need a socket multiplier.