What's wrong with this system?

I have had my current and first real system for about a year. The problem is that a lot of music (especially classical) sounds blah and uninvolving, and I don't think I'm hearing nearly enough details as I should. Here are the components:

-Cambridge Audio D300SE CD player
-NAD C320BEE integrated amp
-Monitor Audio Silver S6 speakers
-Audioquest Diamondback interconnects between the CD player and the amp
-Van Den Hul 'The Clearwater' speaker cable (two 8' runs)

I should mention that my listening area is about 15' x 15' with an 8' ceiling. I would like to 'fix' the system soon, and could spend about $1500 (but wouldn't complain if I didn't have to spend that much, of course!). On a side note, I have been told that tubes would not work with my speakers because the combination would be too warm. Is this true?

Thank you very much for any suggestions you can give me-
I have to agree with Celtic66, I think the Audio Refinement would be an excellent choice. I've seen them used for under 600. That should give you more of the detail and realism that you might be looking for. If it were my system, I wouldn't worry as much about the cables right now. You and I are kind of in the similar stage, and I think your money would be more well spent on amplifier and/or cd player at this point.
I would upgrade your cdp. For $1500 new or used, you will be able to get yourself a cdp that will deliver the goods. Caution! Danger will Robinson, this may lead to an upgrade of additional components down the audio highway. The nature of the audiopool beast in us. peace, warren

Could you share with us setup details of your system / room, i.e. accoustic treatment, vibration tweaks, speaker positioning, rack? floor carpeting...
Take a look at Dirtyragamuffin system and you'll see wall treatment (auralex),power tweaks in other words I'd suggest to check the complete setup to really open the capabilities of your current gear. This could provide a solid foundation to any future upgrade you invest on.
In my book setup is a high priority
Some good advice already. As far as the system goes, I'd agree with Warren: start with the source. I don't think you need to drop the entire $1500 there. As he suggests, you will find that upgrading a single component may lead to revealing faults elsewhere. I would think you can find some source bliss in the $1k range that would still be a significant improvement on your Cambridgge and put aside the balance for the next upgrade. Also, as has been suggested, FIRST look at the room as the source of your problems. A room can make or break even the best of systems, no doubt about it!

Keep the equipment the same for now, and read up and learn about room acoustics, proper system set up techniques and acoustical treatments (which don't always have to be ugly wall panels). Experiment with placement of speakers to try and understand their interaction with the room. Your system is not bad, it probably is just interacting poorly with your room.