Yannick,
You can get a good computer-based system to replace your cd player. The Hollis HAL MS-2 server (about $800) comes with a drive to burn your cd's to a hard drive. There are a lot of good DACs on the market starting from $250 for the Audioquest Dragon. You'd need a monitor, keyboard, 2 drives (one for backup), a DAC, the HAL, and some cables - all of which can be acquired within your budget.
I don't sell any DACs or servers so there's nothing in this for me. Happy hunting!
Scott