A DAC will have digital inputs allowing you to use an inexpensive CD transport in the short-term, maybe even your computer if it has digital audio output and a CD drive, but get good sounding music immediately. Whereas if you focus on researching transports, you will have something to stick CDs into but won't hear any music, or will be using the DAC included with the transport which may not sound good to you.
djones51's recommendation to purchase a VK-D5SE might be your safest and quickest bet, if you can't get a replacement drive for your existing unit.
It may also be worth it to consider repairing your VK-D5 with a replacement drive that isn't the exact same as the original. There's no reason to think it wouldn't sound just as good, as long as a reliable high-quality drive is put in.