What is most important part of a system?

The most important part of any audio system is the person listening to it, and their confirmation bias affected brain.  Also, what they are drinking...

Note:  the OP does not know if the CD and LP were mastered the same...

I think I'll buy one of those T-shirts that says:

IT'S THE TRANSDUCER, STUPID!

It should be obvious to anyone with ANY electronics knowledge at all, that not all parts are critical.  The critical parts are the transducers, e.g. speakers and cartridge if analog.

This why the advice to put half of the budget into speakers is both common and good.  Room treatments are also critical, but are not electronic - they will require some knowledge of acoustics.

The amp needs to be able to drive the speakers, which can be difficult if they are highly reactive or require high current delivery.

The pre-amp is a control center and at the high end can enhance certain euphonic characteristics (tubiness).

The DAC is easy to get good sound from at a few hundred dollars and there is no need to spend $35,000 on it.

But $35,000 spent on speakers can be very worthwhile -- unless you buy Magneplanars for $6,000 and like their advantages over their dis-avantages.

Categorizing importance and quality of components is a good idea because some things are more important than others, and because improvements in some things for a given cost make a larger SQ improvement than other things.

If you built your own listening room (properly) and spent over $25,000 on speakers you are in a different category than someone who spent $850 on speakers.

show me the blind listening test results

another issue is that DAC design is advancing fairly rapidly, esp. compared to loudspeakers

engineers seem to be focusing on noise in DACs, which can cause jitter - not just alter DR and the noise floor

many are saying that noise is being injected from circuits inside as well as outside the DAC

assuming they are at least partly correct, one is likely to have any DAC purchased be a temporary expedient, so buy accordingly

I'd also check out newly marketed DACs that advertise designs with low noise or high noise immunity

NO affiliations with any manfs., dealers, etc. - maybe a few scientists who study sound perception

I am not likely to let big kidz anywhere near my system.

all true, but the real issue is where to spend the most money

that is the way this question is usually interpreted anyway

with digital, that means the only transducer left is the speaker (and as per above, its interface to the room)