A stupid question for which there's no sensible answer.

Giving license to this forum to call your question "idiotic" is like giving license to gravity to pull things down!

I would say "it depends" but it really does depend -- on *how* inferior those other things are to your speakers and amp. And how they are positioned in your room. Because as many have said, even a $100,000 system can sound terrible in the wrong room.

But let’s assume that all the other elements you mentioned are at least decent. I’d say the DAC or the source would make the biggest difference. I added an R2R tube DAC to my existing system before anything else. A DAC that cost $1.1k replaced a $170 DAC and all of a sudden...magic.

It depends not at all....

My answer was obtained after many experiments....

First choose basic good one elements for sure...We must first have an audio system....

After that try to embed these elements rightfully, controlling vibrations, and decreasing the electrical noise floor of the house grid, and try to install controls for all acoustical dimensions of sound in the room...

There is no other road....

Upgrading is the last thing to do before making sure that you already had a good listen to your actual gear working in optimal conditions...

If someone advise someone else for improving his S.Q. to change cable, he is ignorant simply.... Cables make a difference but a small one, especially in a bad embedded system....

Most people have never listen to their system in optimal condition, this is the reason why many throw money unsatisfied...

In general a relatively low cost system may give you a very good audiophile experience contrary to what most audio reviewers will say,because they are paid or unpaid sellers; the only condition is treat and control the acoustic of the room , the vibrations of the gear, and the electrical grid of the room of the house and of the gear....

It is the only thing i know and learn and the rest has no importance for me....Who give a damn to know what is the best costly amplifier in the world if the one you own is relatively good?

My 500 bucks system will give an heart attack to many with very costly one..... They laugh seeing it in my virtual page because people superficially judge things on appearance and price... Not me.....

You dont need money at all.... You need creativity and trust in your ears.....

I used to think your question made sense but then tons of personal experience proved there really is no sensible way of saying anything is any more important than anything else. You want anecdotes? We got anecdotes!  

Complete systems. Besides my own, also put some together for others. When you're doing it for others you have to do what they want not what you want. Turns out after doing it a few times this works out just fine. I was still thinking it must be important to budget roughly equal amounts to have things be around the same level for a balanced result. Which does indeed work really, really good. But then for kicks one time I tried a budget ($1200 total) system with about $2k of interconnect and power cord. The improvement was just as big as when those same things were in my ten times as expensive system.

This holds for everything else as well. Is the power cord going to one component any more or less important than another? Not that I can tell. Is the last 3 feet any more or less important than the first three feet coming out of the panel? Nope. What about the three feet inside the speaker? Not even.  

The problem, I eventually realized, is we are asking the wrong question. Who cares which one has the most influence? Which is just another way of asking Which one is most important? Who cares? What if we know for absolute certain it's the speaker. So what? Does that mean we can forget everything else and put all our money in the speaker? Nope.  

What we really want to know is, Of all the things that matter (which is all of them!) what is the one I can do right now, for the least amount of money, and for the most amount of sound quality improvement? This question no one can answer- except YOU! 

Because the answer depends so much on exactly what you have, and that includes your listening ability and preferences. If you have a wonderful system in every way but bottom end it might be subs. Then again the same guy with the same system might not want that at all. In that case it might be something completely different.  

Know thy system. Know thyself. Figure it out. Best answer I can give you.

Good stuff!

Streamed digital as a source is not currently audiophile quality, but not much can be done, so yes, I would say DAC comes next along with digital cable to that DAC. Then power cord for the DAC.
In other words, get the best source you can and then move downstream.