First, as a general matter, your sound experience is limited by the weakest link. That might be the quality of the original recording (bootleg, Studio, Stereo, mono etc.). It might be the medium that it is stored on (Vinyl, Tape, CD, Etc.). It might be the format used to store (MP3, FLAC, CDA etc.). It that might be the reader (CD rom drive, CD player etc). It might be the audio system (DAC, amp and speakers etc.). It might be the physical environment it is played in (Garage, Bathroom or concert hall etc.) If one piece is significantly weaker than the others it won't matter what you do with those other pieces, you won't notice better sound.
Here is a link to a piece that has some infromation on what the human ear can hear and how the original Red Book CDA digital format came about.
I only say this because making changes to your setup may only make a difference some of the time, the times that the digital to analog conversion process is the weakest link. Having said that, I think that you can improve that process in your setup without a lot of money.
My present setup is a Dell desktop and so I am using the dell internal sound card (known as: High Definition Audio Device). The output is phono plugs with the lead hidden under the carpet edge, round the room, to my audio station (CD, tuner) and amp.
Based upon that, I am assuming that the "High Definition Audio Device" is the on the motherborad audiop that came with your PC. I am also assuming that you are using a converter to convert a headphone output to a RCA (or Cinch as you say in the UK) cable which you connect under the carpet to your Amp to feed it a line level analog signal. In this setup, the on board card's DAC is being used and the audio is being passed through the windows mixer.
If that is the case, if you have a PCI slot available in your PC, you could just get a new PCI high end sound card. The important thing would be to make sure that you get one that can accept ASIO input and has both RCA (Chinch) outputs as well as digital (even though your Amp can't accept digital, you might get one that does in the future). Under this setup you would install the Monkey ASIO plugin and pass the digital output directly to the new sound card and either use its DAC or some day pass the output digitally to your amp/receiver.
I researched different options but settled on the ESI Juli@ card:
I paid $130 for the card and use it to accept the ASIO output from monkey and then use its DAC and connect RCA cables from the Card to my Reciever. I kept the original on board sound card active and use it to play all my computer sounds through computer speakers. To replicate this, all you would need is the Juli@. You could then use the same (Gold no less) cables to send the line level analog to your Amp.
While I think this will be a better setup, You may not notice this unless you get a lossless file of a great recording. Good luck!