Should I buy a new cd player or DAC or both or neither?

Here is my system. I have a Atoll integrated amplifier, 100 wpc, a Vecteur L 4.2 cd player, Totem Hawk speakers, A Cambridge Audio CXN streamer, Nordost Red Dawn speaker cables and Tara Labs interconnects ( not sure of the model but they were $500 Cdn when new).
I am happy with the sound but wonder if I could get better sound (more detailed and dynamic but still warm and easy to listen to), with either a new cd player or DAC or both. My Vector CD  player was really well reviewed by "Enjoy the Music" when it was new but it is 15 years old now. It's built like a tank so it must have a big power supply.  I did have my cd player hooked to an expensive Audiomat Tempo 2.5 DAC but didn't hear an appreciable difference in sound. . I know however the DAC was excellent as the guy I sold it to said it transformed his CD player and it was the best DAC he had ever heard. My Vecteur and Audiomat CD player were supposed to be a good match.

Could it be that my Vecteur CD player is that good?

My local dealer swears he can transform my system with a Atoll DAC which is only $800 Cdn. I also wonder about getting a Marantz CD6006 or a Cyrus CD t (both well reviewed by "What Hi Fi'" or a Cambridge Audio CD as they are available locally. I would consider Oppo too although I would have to order online and could't audition.
I was thinking of potentially spending between 1-2K on a CD player and the same amount on a DAC. Wondering if CD players have improved that much in 15 years? So what should I do? I would welcome any advice or hear from those that have experience with these components.
@audioengr Agreee with your Sony rec.  Do you also have any positive experience running the Sony through a better DAC? Thanks for any ideas along these lines. Love the Sony interface but hoping to improve sound if possible. 
All the ideas are good from fellow audiophiles with regard to getting a streamer or ripper like the Sony, r2r ladder DAC and even new speakers. For sure, you could improve your sound tremendously with better speakers. Vandersteen, Magnepan and even the newer Paradigm are exceptional.
The only thing suggested that I would have reservations about is saying CD players are out dated or the combo of a new transport and DAC cannnot give you really good sound. I mean many people bet the farm that turntables were outdated and vinyl would never come back. Well many people are eating
words, and a much larger group are convinced analog is better than digital. I think CD players will stick around and DACs are getting better. I tend to stream now, and really like MQA but I think record albums still sound fantastic as do some CD players with a good DAC.
Some really like the Bluesound Vault 2, and it does everything you want. I have the Node 2 and it is the best digital sound I have had... for awhile.
You can have both worlds with a DAC. Attach a transport and a streamer.  
2nd the Cambridge CXC. I found big improvement matched with new Wyred4Sound Dac1v2.